MTH 160 Exam 1

Suppose you have two choices for a car loan: $22 interest per $1000 borrowed or $25 interest per $1000 borrowed. Which will result in the lower monthly payment?

$22 per thousand

If the ratio of red jelly beans to blue in a can is 1 to 1 and there are 25 red jelly beans in the can, how many blue jelly beans are in the can?

25 blue jelly beans

A survey of people who liked chocolate or peanut butter found that 52 people like chocolate, 38 people like peanut butter, and 28 people liked both. How many people were in the survey?

52+38=90 90-28=62 in the survey

A car comes with upgrade options that include metallic paint, park assist, blind-spot monitoring, navigation system, sport wheels, and heated seats. How many variations are possible for a person considering this car?

64 options

If the prevalence of a gene is given as 67 per thousand, how many people in a group of 1000 would be expected to have the gene?

67 people

If A and B are two finite, nonempty sets and n(A union B) = n(A)+n(B), what can be said about A and B?

A and B are disjoint — they have no elements in common

If A is a subset of a universal set U, what is (A')' [the compliment of A compliment]

A because the the compliment of A is everything in the universal that is not A so the compliment of the compliment of A would be only the elements in A

You shouldn't vote for him if you advocate women's rights. He has been married and divorced four times.

Ad hominem Premise: He has been married and divorced four times. Conclusion: You shouldn't vote for him if you support women's rights. This is an ad hominem fallacy because the premise is an attack on someone's character rather than the issue.

Give 2 examples of a universal qualifier

All humans are mammals No cat is a dog

The policeman told the kids that eating too much red meat is unhealthy.

Appeal to authority Premise: The policeman stated that eating too much red meat is unhealthy. Conclusion: Eating too much red meat is unhealthy. This is an appeal to authority because it is drawing on expertise from an irrelevant authority.

Parent: I just heard from your principal and she says you were making fun of another student. You're grounded! Child: But everyone else was making fun of her too!

Appeal to common practice Premise: Everyone was making fun of another student. Conclusion: Making fun of another student is acceptable. This is an appeal to common practice because it relies on general acceptance in its premise rather than logic.

The advertisement by Health Food Inc. says that eating the company's nutrition bars keeps you from gaining weight.

Appeal to emotion Premise: Buy Health Food Inc. nutrition bars. Conclusion: If you don't, you will gain weight. This is an appeal to emotion because the argument attempts to connect an emotion to its conclusion.

These shoes will make you run faster because the best running back in the football league endorses them

Appeal to popularity Premise: The best running back in the football league endorses these shoes. Conclusion: They will make you run faster. This is an appeal to popularity because the arguer is attempting to connect a popular figure to the reason for the conclusion.

Today, the temperature dropped 10 degrees from yesterday and I got a headache. Therefore, the temperature drop gave me a headache.

Black-or-white (false dilemma) Premise: Either you protest with us or you are against our cause. Conclusion: You must protest with us so that you are not against our cause. This is a black-or-white fallacy because the premise offers only two choices when in reality there are more.

Draw a Venn diagram to show the set A ∪ (B ∩ C)

Circle A is shaded along with the intersections

This computer is the best because no other computer can compare with its quality.

Circular reasoning Premise: No other computer can compare with the quality of this computer. Conclusion: This computer is the best. This is circular reasoning because the conclusion is the same as the premise, just reworded.

True or False: 49 is a prime number

False

True or False: Some rational numbers are also irrational numbers

False

In 2016, the University of California Los Angeles (UCLA) had an enrollment of 13,361 male and 17,512 female undergraduate students. The total number of full-time instructional faculty was 1848. Find the ratio of students to full-time instructional faculty as a unit

Find the ratio of students to faculty 13,361+17,512/1848 = 30,873/1848 is approximately 17

Three players on our hockey team didn't shave during the playoffs and played much better than usual. Therefore, we should all avoid shaving during the playoffs.

Hasty generalization Premise: Not shaving during playoffs makes you play better. Conclusion: We should all not shave during playoffs. This is a hasty generalization because it assumes that if something is good for a few, then it is good for all.

what phrase is used for implication

If-then ; —>

Use DeMorgan's law to restate "It is raining and the sun is no shining" in an equivalent form

It is not raining, or the sun is shining

Have you told you the teacher that you copied my paper?

Loaded question No premise or conclusion. This is a loaded question because a "yes" or a "no" answer both imply a false or deniable statement.

In the statement "All Ferrari's are red," is the negation of the statement "No Ferrari's are red"

NO. The negative is "some Ferrari's are not red."

If it doesn't rain, the lake will dry up, tourism will decline, the local economy will tank, and we will be forced to move to the city.

Slippery slope Premise: We need more rain. Conclusion: Without it, we will have to move to the city. This is a slippery slope because it assumes many factors in the premise are directly connected when the connection between each factor is actually weak. As the connection between factors weakens, so does the argument.

My math teacher told me that we use math every day, sometimes without even realizing it. I can't believe she thinks we are all mindless zombies

Straw man Premise: Sometimes we use math without realizing it. Conclusion: We are all mindless zombies. This is a straw man fallacy because a new premise was built to distract the audience from the original premise.

A guideline recommended by some financial advisors is that the ratio of the monthly cost for housing to monthly income should be less than 3 to 10. Does a veterinary technician who earns $2700 per month and pays $900 per month for rent meet the recommended guideline?

The veterinary technician's ratio is 900/2700 = 1/3 > 3/10. Therefore, the technician does not meet the guideline.

True or False: -5/3 is a rational number

True

True or False: 0 is a whole number

True

True or False: 5 is an integer

True

True or False: All integers are rational numbers

True

True or False: All rational numbers are real numbers

True

True or False: pi is a real number

True

Can an argument be valid and yet the conclusion be false? Support your answer.

Yes. For instance, "If I like ice cream, all numbers are positive. I like ice cream. Therefore, all numbers are positive." is a valid argument but the conclusion is false.

Suppose C and D are two nonempty sets a. If C is a proper subset of D is it possible that C = D? b. If C is a subset of D is it possible that C = D

a. No because D contains at least one element that C does not b. Yes because C and D could have the exact same elements

Write a negation for each of the following a. some fruit is not good b. no buildings are tall

a. all fruit is good b. some buildings are tall

Let A = {-3,-2,-1,0,1,2,3}, B = {-6,-4,4,6} and C = {-2,0,2,4,6}. Find a. A ∩ B b. A ∩ C

a. empty set b. {-2,0,2}

Let A = {4,6,8,9,10,12}. For each of the following answer true or false: a. {4,8,12} ⊂ A b. {6,7,8} ⊂ A c. empty set ⊆ A d. {6} ⊆ A

a. true b. false c. true d. true

determine whether each sentence is a statement a. My sister's birthday is next Sunday b. Do you run marathons?

a. yes because it states a fact b. no it asks a question

Let A = {-3,-2,-1,0,1,2,3}, B = {-6,-4,4,6} and C = {-2,0,2,4,6}. Find a. A ∪ B b. A ∪ C

a. {-6,-4,-3,-2,-1,0,1,2,3,4,6} b. {-3,-2,-1,0,1,2,3,4,6}

what word is used for conjunction

and ; ∧

Identify the antecedent and the consequent of the statement "If the snow begins to fall, I will not go skiing"

antecedent - the snow begins to fall consequent - i will not go skiing

a television advertisment shows a lively party with everyone drinking a popular beverage. what type of fallacy might this be

appeal to common practice fallacy

Even though we have proven that the jewelry she's wearing is yours, we have not proven that she stole it from you. Therefore, she did not steal it from you

appeal to ignorance

an advertisement shows a picture of a famous actor next to a new car. What type of fallacy might this be?

appeal to popularity fallacy

write the compound statement in symbolic form: "The tea was cold (c) and sweet (s)

c ∧ s

When a person with chicken pox is given a test for chicken pox, the test comes back positive. This is an example of a _________

correct outcome

If p is a true statement and q is a false statement what is the truth-value of p ∧ q

false

When a person with chicken pox is given a test for chicken pox, the test comes back negative. This is an example of a _________

false negative

write the inverse, converse, and contrapositive for the conditional " if it is snowing, I will not go skiing"

inverse - if it is not snowing, then i will go skiing converse - if i do not go skiing, the snow will fall contrapositive - if i go skiing, it will not snow

an associate asks whether you have stopped making inappropriate comment to coworkers. what type of fallacy might this be

loaded question fallacy

what word is used for disjunction

or ; ∨

child: it's really hard to make a living on the salary i earn parent: when i was your age i only made $80 a week

red herring fallacy premise: i only made 80 per week when i was your age conclusion: therefore it should not be hard to make a living on your salary this is a red herring fallacy because the premise is an attempt to distract the audience from the original statement

give 2 examples of an existential qualifier

some pets are small some pets are not dogs

write the negation of "The color of the wall was not red"

the color of the wall was red

Using p to represent "The stock market went up" and q to represent "The bond market went down" write p v (~q)

the stock market went up or the bond market did not go down

If p is a true statement and q is a false statement what is the truth value of p ∨ q

true

Determine the truth-value of the conditional "If diamonds are emeralds, then 7 = 8"

true it is a double negative

Is 25 miles per gallon of gas a unit rate

yes because you are measuring two different quantities (miles/gallons)

Let U = {natural numbers less than 20} and P = {prime numbers less than 20}. Find P'

{1,4,6,8,9,10,12,14,15,16,18}

Use the roster method to list the natural numbers less than 20 that are divisible by 3

{3,6,9,12,15,18}