7.9.8: Review Exercises

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Exercise 1

1. State George Polya's Four Step Problem Solving Process. Only list the 4 headings.

Exercise 2

2. State 4 strategies for Devising a Plan.

Exercise 3

3. Juan will give you $1 on the first day of April, $2 on the second day of April, $4 on the third day of April, and double the amount through April 15^th, or he will give you $30,000 up front on the first day of April. Which is the better deal and why?

Exercise 4

4. Find the next three numbers in the sequence:

a. 0, 10, 10, 20, 20, 20, 30, 30, 30, 30, 40,

b. 5, 15, 45, 135,

Exercise 5

5. List the ways you can make change for $25 using $5, $10, and $20 bills.

Exercise 6

6. Explain the difference between inductive and deductive reasoning.

Exercise 7

7. State whether each of the following is a proposition are not. If not, state why not. If it is a proposition, state its truth value.

a. 3 + 4 = 7

b. California is not in the U.S.

c. Mary is pretty.

Exercise 8

8. Determine whether each quantified statement is true or false.

a. All men have black hair.

b. Some women have blond hair.

c. No boys like pigs.

Exercise 9

9. State the negation of each statement.

a. Grass is green.

b. Tim married Tom.

c. It is not cold outside.

Exercise 10

10. State the negation of each quantified statement.

a. Everyone plays Pokemon Go.

b. Some kids wear hats.

c. No dogs jump on the couch.

Exercise 11

11. If p is true and q is false, state the truth value of each of the following.

a. $p \land q$

b. $p \lor (~ q)$

c. p → q

d. q → p

e. ~$(p \lor q$)

Exercise 12

12. Negate each statement.

a. I am married if I wear a wedding ring.

b. It is hot outside and I am at the beach.

c. My name is Julie or my name is Beth.

Exercise 13

13. State the converse, inverse, and contrapositive of this conditional.

“If Omar doesn’t buy cat food, then Omar owns a fish.

Exercise 14

14. Determine if the following arguments are valid or not. If they are valid, write if it is by Modus Ponens, Modus Tollens, or the Chain Rule. If it is not valid, write if it is by Fallacy by Converse Error, or Fallacy by Inverse Error, or neither. If it looks like the chain rule, but has a false conclusion, write the correct conclusion.

If you are a child then you are not a legal adult.

Sean isn’t a legal adult.

Sean is a child.

If you drink wine, then you are at a bar.

Marsha is at a bar.

Marsha drinks wine.

If you eat hot dogs, then it is $4^{\text{th}}$ of July.

It is $4^{\text{th}}$ of July.

You are eating hot dogs.

If you like vegetables, then you are vegan.

Beth is not vegan.

Beth does not like vegetables.

If you are in college, then you have a car.

If you have a car, then you know how to drive.

If you are in college, then you know how to drive.

Exercise 15

15. Write a conclusion to make each argument valid. State if you used Modus Ponens or Modus Tollens.

If you eat worms, then you are a fish.

Matt is not a fish.

If you have a certificate, then you have a job.

Isabel has a certificate.

Exercise 16

16. What is a tautology? What is a fallacy?

Exercise 17

17. Make a truth table for the following. State if it is a tautology, fallacy, or neither.

a. p → $(p \lor q$)

b. ~($p land q) → ~q$

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