MATH 1100

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A perfect number is a natural number that is equal to the sum of its​ factors, excluding the number itself. Determine whether or not the given number is perfect. 32

32 is not a perfect number (no)

greatest common divisor of 99 and 66 is

33

1/3 =

33.33%

greatest common divisor of 105 and 385

35

(-6)^2

36

least common multiple of 126 and 189

378

prime factorization of 675

3^3*5^2

prime factorization of the composite number 16,524

3^5*2^2*17

2/7 x 2/7 =

4/49

5/27 + 2/15 =

43/135

4/9 =

44.4%

To express 3/10 as a​ percent, divide​ ______ by​ ______, multiply the quotient by​ ______, and attach a percent sign.

3 ; 10 ; 100

Write the​ converse, inverse, and contrapositive of the statement below. ~r→q

converse: q → ~r inverse: r → ~ q contrapositive: ~q→r

6 serves as​ a/an _______ to the conjecture that the sum of two odd numbers is an odd number.

counterexample

To find the discount​ amount, multiply the _________ and the ________________

discount rate ; original price

If you are selecting the best investment from two or more​ investments, the best choice is the account with the greatest​ _______, which is the​ __________ interest rate that produces the same amount of money at the end of one year as when the account is subject to compound interest at a stated rate.

effective annual yield ; simple

The symbol ∈ is used to indicate that an object is an _________________ of a set.

element

A set that contains no elements is called the​ _______ set and is represented by​ _______.

empty/null ; Ø = { }

Two sets that contain exactly the same elements are called __________ sets

equal

Two sets that contain the same number of elements are called​ _______.

equivalent

​p: It is time to sleep. ​q: The taxes are high. Write the symbolic statement ​ ~ ( q ∨ p ​) in words.

it is not true that the taxes are high or it is time to sleep

​p: It is time to sleep. ​q: The chair is broken. Write the symbolic statement p ↔ ​~q in words.

it is time to sleep if and only if the chair is not broken

The smallest number that is divisible by two or more natural numbers is called their​ _______.

least common multiple

If a​ < b, then a is located to the of b on a number line.

left

you did not do the dishes and you left the car a mess

let p= you did the dishes and let q = you left the car a mess; ~p∨q

p: The shoe is grey. ​q: The belt is tan. Write the symbolic statement p∨~q in words.

the shoe is grey or the belt is not tan

greatest common divisor of 16 and 30

2

1/5 =

20%

A perfect number is a natural number that is equal to the sum of its​ factors, excluding the number itself. Determine whether or not the given number is perfect. 26

26 is not a perfect number (no)

least common multiple of 90 and 54

270

prime factorization of the composite number 6804

2^3 × 5× 17

prime factorization of 88

2^3*11

prime factorization of 24

2^3*3

simplify √24

2√6

greatest common divisor of 27 and 75

3

To negate a​ disjunction, negate each of the component statements and change​ "or" to​ _____.

"and"

To negate a​ conjunction, negate each of the component statements and change​ "and" to​ _____.

"or"

20√13 + 23√13 =

(20+23)√13 = 43√23

28√3 + 30√3 =

(28+30)√3 = 58√3

44√7 + 47√7 =

(44 +47) = 91√7

​p: The chair is broken. ​q: It is snowing outside. ​r: It is Tuesday. Write the following compound statement in its symbolic form. The chair is broken and it is snowing outside​, or it is Tuesday

(p∧q)∨r

counterexample that shows that the following statement is false if a number is added to itself, the sum is greater than the original number

-3 + (-3) = -6

(-4)^3

-64

3/8%

0.00375

1/2%

0.005

7/8%

0.00875

Use the percent​ formula, A=PB​: A is P percent of​ B, to answer the following question. What is 3% of 600​?

0.03 x 600 = 18

Use the percent​ formula, A=PB​, where A is P percent of​ B, to answer the following question. What is 17% of 20​?

0.17 x 20 = 3.4

42.6%

0.426

76%

0.76

counterexample that shows that the following statement is false adding the same number to both the numerator and the denominator (top and bottom) of a fraction does not change the fraction's value

1+1 /2+1 = 2/3; the fraction 2/3 is not equal to 1/2

greatest common divisor of 70 and 50 is

10

Percents are the result of expressing numbers as a part of ________

100

simplify 5√20

10√5

simplify √500

10√5

A perfect number is a natural number that is equal to the sum of its​ factors, excluding the number itself. Determine whether or not the given number is perfect. 12

12 is not a perfect number (no)

Suppose you have $14,000 to invest. Which of the two rates would yield the larger amount in 2 years​: 12​% compounded daily or 11.92% compounded​ continuously? Which of the two rates would yield the larger amount in 2 years​?

12​% compounded daily

greatest common divisor of 195 and 30

15

A perfect number is a natural number that is equal to the sum of its​ factors, excluding the number itself. Determine whether or not the given number is perfect. 15

15 is NOT a perfect number (no)

A prime number is an emirp​ ("prime" spelled​ backward) if it becomes a different prime number when its digits are reversed. Determine whether or not the given prime number is an emirp. 173

173 is not an emirp (no)

simplify 7√175

175= 7*25 √7 *√25 √25= 5 7√175 = 7(5)√7 answer: 35√7

least common multiple of 60 and 45

180

absolute value: |2|

2

A perfect number is a natural number that is equal to the sum of its​ factors, excluding the number itself. Determine whether or not the given number is perfect. 45

45 is not a perfect number (no)

least common multiple of 156 and 117

468

simplify √80

4√5

counterexample that shows that the following statement is false if a number is multiplied by itself, the result is even

5*5 = 25

0.52

52%

0.5235

52.35%

simplify √54

54 = 6*9 largest perfect square that is a factor of 54 is 9 √54 = √6*9 = √6*√9 √9 = 3 answer: 3√6

25/4 mixed number

6 1/4

A perfect number is a natural number that is equal to the sum of its​ factors, excluding the number itself. Determine whether or not the given number is perfect. 6

6 is a perfect number (yes)

3/50

6% 3 / 50 = 0.06 x 100 = 6

Suppose you have $10,000 to invest. Which of the two rates would yield the larger amount in 5 years​: 7​% compounded monthly or 6.86% compounded​ continuously?

7​% compounded monthly

The three sets in the Venn diagram will separate the universal set into ____ regions

8

4/5 =

80%

√9 * √9

9

98 =

9800%

Suppose you have $15,000 to invest. Which of the two rates would yield the larger amount in 1 year​: 9​% compounded quarterly or 8.89% compounded​ continuously? Which of the two rates would yield the larger amount in 1 year​?

9​% compounded quarterly

If interest is compounded once a​ year, the formula that gives the​ money, A, in an account after t years at rate r is​ _______, where P is the original principal.

A=P(1+r)t​,

The future​ value, A, of P dollars at simple interest rate r for t years is given by the formula

A=P(1+rt)

The statement​ "No A are​ B" can be expressed equivalently as​ _______.

All A are not B.

A rule that allows financial institutions to calculate simple interest using 360 days in a year is called the​ _______ rule.

Banker's Rule

Write the​ converse, inverse, and contrapositive of the statement below. If wax will get on the furniture​, then dripless candles do not drip.

Converse: if dripless candles drip do not drip, then wax will get on the furniture. Inverse: if wax will not get on the furniture, then dripless candles drip. Contrapositive: if dripless candles drip, then wax will not get on the furniture.

Use De​ Morgan's laws to write a statement that is equivalent to the following statement. It is not true that parrots or ostriches can fly.

If parrots can fly, then ostriches can not fly

Write the negation of the statement below. He is not hungry and I am hungry.

He is hungry or I am not hungry

If high blood pressure is not desirable, then many people are alarmed.

High blood pressure is not desirable and many people are not alarmed

Conditional Statement: If I am in Los Angeles​, then I am in California.

I am in Los Angeles and I am not in California

​p: I get a raise. ​q: I do my homework. Write the following symbolic statement in words ​~p↔q

I don't get a raise if and only if I do my homework

The formula for calculating simple​ interest, I, is​ _______, where P is the​ _______, r is the​ _______, and t is the​ _______.

I=Prt ; principal ; rate ; time

The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. P​ = ​$7000​, r​ = 5​%, t​ = 1 year

Interest = principal x rate x time 7000 x 0.05 x 1 = $350

Form the negation of the statement. Monday does not come after Sunday

Monday comes after Sunday

What is the negation of​ "Some A are​ B"?

No A are B.

What can the statement​ "Some A are not​ B" be expressed equivalently​ as?

Not all A are B.

in the formula A=P[(1+r/n)^nt−1] / (r/n)​, _______ is the deposit made at the end of each compounding​ period, ________ is the annual interest rate compounded ______ times per​ year, and A is the ______ after _____ years

P ; r ; n ; value of the annuity ; t

n the formula P=A/(1+rn)^nt​, the variable​ _______ represents the amount that needs to be invested now in order to have​ _______ dollars accumulated in​ _______ years in an account that pays rate​ _______ compounded​ _______ times per year.

P, A, t, r, n

p→q can be translated as​ "p is necessary for​ q."

The statement is false because p → q means​ "p is sufficient for​ q," so q can still occur even if p does​ not, but if p​ occurs, so does q.

The negation of​ "All A are​ B" is​ _______.

Some A are not B.

The following statement is false. ​r: All Americans have German ancestry. Use the representation of r to express the symbolic statement​ ~r in words. Verbal statements should begin with​ "all," "some," or​ "no." What can you conclude about the resulting verbal​ statement?

Some Americans do not have German ancestry ; the resulting verbal statement is true

The following statement is false. ​p: No planets are larger than earth. Use the representation of p to express the symbolic statement​ ~p in words. Verbal statements should begin with​ "all," "some," or​ "no." What can you conclude about the resulting verbal​ statement?

Some planets are larger than earth ; the resulting verbal statement is true

p ∨ q means p or​ q, but not both.

The statement is false because the connective ∨ is an inclusive​ or, which means​ "either or​ both."

the collection of current NFL players the collection of US airports

The collection is well defined and therefore it is a set.

A = {2,2,2,4,4,6,8,10} B = {10,8,6,4,2}

The sets are equivalent because n(A)=​n(B) The sets are equal because set A contains the exact same elements as set B.

A is the set of cities in a regions B is the set of people who are now mayors of the cities in that region

The sets are equivalent because they contain the same number of elements. The sets are not equal because they do not contain the exact same elements.

Use a truth table to determine whether the statement below is a​ tautology, a​ self-contradiction, or neither. [(q→p)∧~p]→~q

The statement [(q→p)∧~p]→~q is a tautology.

If set A is a proper subset of set​ B, the sets are represented by two circles where circle A is drawn outside of circle B.

The statement is false. If set A is a proper subset of set​ B, the sets are represented by two circles where circle A is drawn inside of circle B.

Determine whether the statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement. A conditional statement is false only when the consequent is true and the antecedent is false

The statement is false. The true statement​ is, "A conditional statement is false only when the antecedent is true and the consequent is​ false."

Determine whether the following statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement. If one component statement in a conjunction is​ false, the conjunction is false.

The statement is true because a conjunction is true only when both component statements are true.

It can be proved that (A∩B)′=A′∪B′​, so this means that the complement of the intersection of two sets is the union of the complement of those sets

The statement is true because a theorem is always true and (A∩B)′=A′∪B′ means that the complement of the intersection of two sets is the union of the complement of those sets.

p↔q can be translated as​ "p is necessary and sufficient for​ q."

The statement is true because the biconditional statement p ↔ q means p → q​, so p is sufficient for​ q, and q → p​, so p is necessary for q.

The consequent is the necessary condition in a conditional statement.

The statement is true because the conditional statement p → q means​ "q is necessary for​ p" and q is the consequent.

Equal sets are represented by the same circle.

The statement is true.

The statement​ "All A are​ B" can be expressed equivalently as​ _______.

There are no A that are not B.

What can the statement​ "Some A are​ B" be expressed equivalently​ as?

There exists at least one A that is a B.

When the number of compounding periods in a year increases without​ bound, this is known as​ ___________ compounding.

continuous

Use De​ Morgan's laws to write a statement that is equivalent to the following statement. It is not true that Tom and Jerry are both friends.

Tom is not a friend or Jerry is not a friend

Visual relationships among sets are shown by

Venn diagrams

The statement listed below is false. Let p represent the statement. ​p: A baryon is a particle composed of seven quarks. Express the symbolic statement ​~p in words. What can be concluded about the resulting verbal​ statement?

a baryon is not a particle composed of seven quarks ; the resulting verbal statement is true because p is false

Two integers that have the same absolute​ value, but lie on opposite sides of zero on a number​ line, are called

additive inverses

{15, 16, 17, 18,....}

all natural numbers greater than 14

A sequence of equal payments made at equal time periods is called​ a/an

annuity

a. Express the quantified statement in an equivalent​ way, that​ is, in a way that has exactly the same meaning. b. Write the negation of the quantified statement.​ (The negation should begin with​ "all," "some," or​ "no.") Some integers are

at least one integer is a number ; no integers are numbers

A​ disjunction, p∨​q, is false only when​ _______

both p and q are false

A​ conjunction, p ∧ q​, is true only when

both p and q are true

The number that multiplies a square root is called the square​ root's _______.

coefficient

The set of all elements in the universal set that are not in set A is called the​ _________ of set​ A, and is symbolized by​ _________.

complement ; A'

A natural number greater than 1 that is divisible by a number other than itself and 1 is called​ a/an ______ number.

composite

Compound statements that are made up of the same simple statement and have the same corresponding truth values for all​ true-false combinations of these simple statements are said to be​ _______, connected by the symbol​ _______.

equivalent, ≡

Determine the truth value for the following statement when p is false and q is false. ​~(q→p​)

false

The negation of a true statement is a ____________ statement and the negation of a false statement is a ____________ statement.

false ; true

The largest number that is a factor of two or more natural numbers is called their

greatest common divisor

r: They raise monkeys. s​: She has a pet turtle. Write the symbolic statement r→​~s in words.

if they raise monkeys, then she does not have a pet turtle

​p: The temperature is below 30°. ​q: We finished writing. ​r: We go to the slope. Write the symbolic statement (q∧r)→p in words. If the symbolic statement is given without​ parentheses, statements before and after the most dominant connective should be grouped. Translate into English.

if we have finished writing and we go to the slope, then the temperature is below 30°

the number 17/5 is an example of a/an _________ fraction because ___________________________

improper; the numerator

Arriving at a general conclusion based on observations of specific examples is called _______________ reasoning

inductive

Arriving at a general conclusion based on observations of specific examples is called​ _______.

inductive reasoning

In order to perform set operations such as (A ∪ B) ∩ (A ∪ C)​, begin by performing any set operations​ ________

inside parentheses

The set of elements common to both set A and set B is called the __________ of sets A and​ B, and is symbolized by __________

intersection; A ∩ B

A prime number is an emirp​ ("prime" spelled​ backward) if it becomes a different prime number when its digits are reversed. Determine whether or not the given prime number p is an emirp. 43 The given​ number, p=43​, ________ an emirp because the number formed when the digits of p are​ reversed, ___________ enter your response here​, is _______

is not ; 34 ; composite

​q: It is July 4th. ​r: We are having a barbeque. Write the symbolic statement q∧~r in words.

it is July 4th and we are not having a barbeque

Conditional Statement: If it is blue​, then it is not a carrot.

it is blue and it is a carrot

Form the negation of the statement. it is below zero outside

it is not below zero outside

Form the negation of the statement. it is snowing

it is not snowing

​p: I get an A. ​q: It is time to sleep. Write the symbolic statement ​~ ( p ∧ q) in words

it is not true that I get an A and it is time to sleep

​p: I work hard. ​q: It is snowing outside. Write the symbolic statement ​~ ( p ∧ q​ ) in words.

it is not true that I work hard and it is snowing outside

Use De​ Morgan's laws to write a statement that is equivalent to the following statement. It is not true that the bat or ball are red.

it is not true that the bat or ball are red

The statement listed below is false. Let p represent the statement. ​p: Listening to classical music makes infants smarter. Express the symbolic statement ​~p in words. What can be concluded about the resulting verbal​ statement?

listening to classical music does not make infants smarter ; the resulting verbal statement is true because p is false

b. b. Represent the original number as n​, and use deductive reasoning to prove the conjecture in part​ (a).

multiply the number by 2 2n add 8 to the product 2n+8 divide the sum by 2 1n +4 subtract 4 from the quotient 1n

The formula for the cardinal number of elements in set A or set B is n(A∪B)=

n(A) + n(B) - n(A∪B)

The set of {1,2,3,4,5} is called the set of ____________.

natural numbers

take a right at Cross Street is a statement?

no, because it is a command

3 | 8765

no, because the sum of the digits is not divisible by 3

​~p has the​ _______ truth value from p.

opposite

Compound interest is interest computed on the​ _______ as well as on any accumulated​ _______.

original principal ; interest

A conditional​ statement, p → q​, is false only when

p is true and q is false

p: This is a kiwi. ​q: This is a fruit. Write the following compound statement in symbolic form. If this is a kiwi​, then this is a fruit.

p → q

The compound statement​ "If p, then​ q" is symbolized by​ _______ and is called a​ _______.

p → q ; conditional

​p: You are human. ​q: You have fins. Write the following compound statement in symbolic form. You do not have fins if you are human.

p → ~q

The compound statement​ "p if and only if​ q" is symbolized by ________ and is called​ a/an __________.

p ↔ q ; biconditional.

The compound statement​ "p and​ q" is symbolized by​ _______ and is called a​ _______.

p ∧ q ; conjunction

p: 5 + 2 = 7 q: 10 x 2 =40 p ∧ q

p ∧ q is false

p: it is Tuesday q: I work hard Write the following compound statement in its symbolic form. It is Tuesday and I do not work hard.

p ∧ ~ p

The negation of p → q is​ _____. To form the negation of a conditional​ statement, leave the ​ _____ unchanged, change the "if-​then" connective to​ _____ and negate the​ _____.

p ∧ ~q ; antecedent; "and," ; consequent

p: the stove is hot q: it is time to sleep the stove is hot or it is time to sleep symbolic form is

p ∨ q

The compound statement​ "p or​ q" is symbolized by ________ and is called​ a/an ________

p ∨ q; disjunction

A natural number greater than 1 that has only itself and 1 as factors is called​ a/an __________ number

prime

​p: The store is closed. ​q: It is Sunday. Write the following compound statement in symbolic form. The store is closed if and only if it is Sunday

p↔︎q

Write the following compound statement in its symbolic form. It is Tuesday and I eat bananas.

p∧q

Cancer and Capricorn Tuesday and Thursday

the set of zodiac signs that begin with C the set of weekdays that begin with T

p : 3 + 6 = 8 q: 5 x 4 = 20 p∨q

p∨q is true

p: 5 + 9 = 14 q: 5 x 3 = 15 p∨~q

p∨~q is true

the converse of p→q is​ _______.

q → p

Statements that contain the words all​,some​, and no are called ________________ statements.

quantified

p: I'm happy q: you're angry Write the following compound statement in symbolic form. You're angry, but I'm not happy.

q∧~p

​p: I eat bananas. ​q: It is time to sleep. ​r: I study. Write the following compound statement in its symbolic form. I study​, if and only if I eat bananas and it is not time to sleep.

r ↔︎(p∧~q)

The set of​ _______ is the set of all numbers which can be expressed in the form a/b​, where a and b are​ _______ and b is not equal to​ _______.

rational numbers; integers; zero

The quotient of two fractions is the product of the first number and the ______________________ of the second number.

reciprocal/multiplicative inverse

Use De​ Morgan's laws to write a statement that is equivalent to the following statement. ​~(~r∨~p​)

r∧p

counterexample that shows that the following statement is false No US president has been younger than 65 at the time of his inauguration

select the presidents that were younger than 65

a. Express the following quantified statement in an equivalent​ way, that​ is, in a way that has exactly the same meaning. b. Write the negation of the following quantified statement.​ (The negation should begin with​ "all," "some,​ " or​ "no.") Not all math tests are

some math tests are not fun ; all math tests are fun

The formula A=P(1+r/n)^nt gives the amount of​ money, A, in an account after​ ____ years at rate​ ____subject to compound interest paid​ ____times per year.

t , r , n

To find the sales tax​ amount, multiply the ____________ and the _______________

tax rate ; item's cost

√1091 = 33.0302

tenth = 33 hundredth = 33.03 thousandth = 33.030

The numerator of the fraction for percent decrease is the amount of decrease and the denominator of the fraction for percent decrease is the original amount

the amount of decrease; the original amount

The numerator of the fraction for percent increase is ________________ and the denominator of the fraction for percent increase is __________________

the amount of increase; the original amount.

Use De​ Morgan's laws to write a statement that is equivalent to the following statement. It is not true that the apple and orange are both citrus fruits.

the apple is not a citrus fruit or the orange is not a citrus fruit

Use De​ Morgan's laws to write a statement that is equivalent to the following statement. It is not true that the baby or puppy want to go outside.

the baby does not want to go outside and the puppy does not want to go outside

On a number​ line, the absolute value of​ a, denoted​ |a|, represents​ _______.

the distance from 0 to a

​p: The job pays well. ​q: It is snowing outside. Write the symbolic statement ​~p ∧ q in words.

the job does not pay well and it is snowing outside

a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as n.

the result of the 1st number = 2 follow the procedure 2n + 8 10 / 2 = 5 5- 4 = 1 answer: 1n

The set​ {California, Colorado,​ Connecticut} is expressed using _______________. The set​ {x|x is a U.S.state whose name begins with the letter​ C} is expressed using ________________.

the roster method ; the roster method.

The following statement is false. ​r: The speed of light is not constant. Use the representation of r to express the symbolic statement​ ~r in words. What can you conclude about the resulting verbal​ statement?

the speed of light is constant ; The resulting verbal statement is true.

Disjoint sets are represented by circles that do not overlap.

the statement is true

p is true​, q is false​, and r is true p ∧ (q∨r)

the statement is true

p→q can be translated as​"p is sufficient for ​q."

the statement is true

p↔q can be translated as​"If p thenq . , and if q then ​p."

the statement is true

p∧q can be translated as​"p but​q."

the statement is true

Use a truth table to determine whether the two statements are equivalent. ~p→~q and ~q → ~p

the statements are not equivalent

​p: I study. ​q: The stove is hot. Write the symbolic statement ​~ q ∨ p in words.

the stove is not hot or I study

Let p=The woman is pretty. Let q=She earns​ $230,000 more on average in her lifetime. Write in words the meaning of the following statement. ~p ∧ q

the woman is not pretty and earns $230,000 more on average in her lifetime

a. Express the quantified statement in an equivalent​ way, that​ is, in a way that has exactly the same meaning. b. Write the negation of the quantified statement.​ (The negation should begin with​ "all," "some," or​ "no.") All cars are red.

there are no cars that are not red ; some cars are not red

a. Express the quantified statement in an equivalent​ way, that​ is, in a way that has exactly the same meaning. b. Write the negation of the quantified statement.​ (The negation should begin with​ "all," "some," or​ "no.") All integers are numbers.

there are no integers that are not numbers ; some integers are not numbers

Conditional Statement: If there is a hurricane, then all restaurants are closed

there is a hurricane and some restaurants are not closed

Conditional Statement: If there is an earthquake, then all schools are closed

there is an earthquake and some schools are not closed

f compound interest is paid four times per​ year, the compounding period is​ ____ month(s) and the interest is compounded​ ____.

three ; quarterly

Determine the truth value for the following statement when p is false and q is true. ​~(q→p​)

true

Determine the truth value for the given statement when p is false and q is false. ~p↔︎q

true

Determine whether the statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement. If one component statement in a disjunction is​ true, the disjunction is tru

true

A statement is a sentence that is​ _______ or​ _______, but not both simultaneously.

true ; false

To express 7.3​% as a​ decimal, move the decimal point _______ places to the ________ and ______________

two ; left ; remove the percent sign

To express 0.1 as a​ percent, move the decimal point ______ place(s) to the __________ and attach __________________________

two ; right ; percent sign

The set of elements that are members of set A or set B or of both sets is called the​ _________ of sets A and​ B, and is symbolized by​ _________.

union ; A∪B

​p: The temperature is above 70°. ​q: We finished writing. ​r: We go to the pool. Write the symbolic statement r∧(q→p) in words. If the symbolic statement is given without​ parentheses, statements before and after the most dominant connective should be grouped. Translate into English.

we go to the pool, and if we have finished writing then the temperature is above 70°.

Stacy ate all of her spinach is a statement

yes, because it could be labeled as true or false

santa claus is real

yes, because the sentence can be either true or false, but both simultaneously

Christmas come twice a year

yes, because the sentence can be either true or false, but not both simultaneously

A triangle has four sides

yes, because the sentence can be either true or false, but not simultaneously

9 | 29,124

yes, because the sum of the digits is divisible by 9

The integers are defined by the set​ _______.

{...,-3,-2,-1,0,1,2,3,...}

p : 10 + 10 = 20 q: 5 x 5 = 25 ~ p ∧ q

~ p ∧ q is false because p does equal 20

Let p and q represent the following statements. ​p: The fire is burning. ​q: Christmas does not come twice a year. Express the following statement symbolically. The fire is not burning.

~p

Let r represent the following statement. p​: One works hard. Express the statement One does not work hard symbolically.

~p

The negation of statement p is expressed by writing​ _______. We read this as​ _______.

~p ; not p

De​ Morgan's laws state that​ ~(p∧q)≡_____ and​ ~ (p∨q) ≡_____.

~p ∨ ~ q ; ~p ∧ ~ q

The inverse of p → q is​ ________.

~p→~q

​p: This is a gorilla. ​q: This is a mammal. Write the following compound statement in symbolic form. If this is not a gorilla​, then this is not a mammal.

~p→~q

p : 9 + 10 = 18 q: 5 x 3 = 15 ~p∧~q

~p∧~q is false

p: 10 + 5 = 15 q: 2 x 3 = 6 ~p∨~q.

~p∨~q is false

p: 2 + 7 = 9 q: 7 x 6 = 84 ~p∨~q

~p∨~q is true

q: 7 x 6 = 42 ~q

~q is false

p: You are human. ​q: You have antlers. Write the following compound statement in symbolic form. Being human is necessary for not having antlers.

~q → p

The contrapositive of p → q is​ ________.

~q→ ~p

p: I complete my homework. ​q: I get a promotion. Write the following compound statement in symbolic form. I do not get a promotion if and only if I do not complete my homework.

~q↔︎~p

p: I'm leaving q: you're leaving Write the following compound statement in symbolic form. You're not leaving, but I'm staying.

~q∧p

Let r represent the following statement. r​: One works hard. Express the statement One does not work hard symbolically.

~r

Negation of the following statement ~r→~q

~r∧q

The irrational number​ _______ represents the circumference of a circle divided by the diameter of the circle.

π

As the number of elements in a set​ increases, larger circles are needed to represent the set.

​False, the size of a circle does not need to be proportional to the number of elements in its corresponding set.

Some women have served as U.S. senators is a statement

​Yes, because the sentence can be either true or​ false, but not both simultaneously.

√11 * √15 =

√165

√16⋅21 =

√16⋅√21 =4√21

The square root of​ n, represented by​ _____, is the nonnegative number that when multiplied by itself gives​ _____.

√n ; n


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