MATH 1100
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 butq."
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
