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Same stuff, answer the questions like you did before and try to make it as good as you can I need at least a 90 out of 100, so please make sure your right! THANK YOU

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Unit 3 Exam – Logic

MATH 105

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write the compound statement in symbols.

Let r = “The food is good.”

p = “I eat too much.”

q = “I’ll exercise.”

1) If the food is not good, I won’t eat too much.

A) ~(r p)

B) ~r ~p

C) r ~p

D) ~p

1)

~r

Write the converse, inverse, or contrapositive of the statement as requested.

2) If I pass, I’ll party.

Contrapositive

A) If I party, then I passed.

C) If I don’t party, I didn’t pass.

2)

B) If I don’t pass, I won’t party.

D) I’ll party if I pass.

3) If I were young, I would be happy.

3)

Converse

A) If I were happy, I would be young.

B) If I were young, I would not be happy.

C) If I were not happy, I would not be young.

D) If I were not young, I would not be happy.

4) All cats catch birds.

4)

Inverse

A) If it’s not a cat, it doesn’t catch birds.

C) If it doesn’t catch birds, it’s not a cat.

B) Not all cats catch birds.

D) If it catches birds, it’s a cat.

Let p represent the statement, “Jim plays football”, and let q represent the statement “Michael plays basketball”. Convert

the compound statement into symbols.

5) Jim does not play football and Michael plays basketball.

5)

A) ~p q

B) ~(p q)

C) ~p q

D) p q

Use De Morgan’s laws to write the negation of the statement.

6) Cats are lazy or dogs aren’t friendly.

A) Cats aren’t lazy or dogs aren’t friendly.

B) Cats aren’t lazy or dogs are friendly.

C) Cats aren’t lazy and dogs are friendly.

D) Cats are lazy and dogs are friendly.

Write the compound statement in words.

Let r = “The puppy is trained.”

p = “The puppy behaves well.”

q = “His owners are happy.”

7) r (p q)

A) The puppy is trained, the puppy behaves well, and his owners are happy.

B) If the puppy is trained and the puppy behaves well, then his owners are happy.

C) If the puppy is trained, then the puppy behaves well and his owners are happy.

D) The puppy is trained and the puppy behaves well if his owners are happy.

1

6)

7)

Write the negation of the conditional. Use the fact that the negation of p q is p ~q.

8) If you give your hat to the doorman, he will give you a dirty look.

A) You do not give your hat to the doorman and he will give you a dirty look.

B) If you give your hat to the doorman he will not give you a dirty look.

C) You do not give your hat to the doorman and he will not give you a dirty look.

D) You give your hat to the doorman and he will not give you a dirty look.

Convert the symbolic compound statement into words.

9) p represents the statement “It’s Monday.”

q represents the statement “It’s raining today.”

Translate the following compound statement into words:

~p ~q

A)

B)

C)

D)

9)

It’s not Monday and it’s not raining today.

It’s not the case that it’s Monday and raining today.

It’s not Monday or it’s not raining today.

It’s Monday or it’s raining today.

10) p represents the statement “It’s raining in Chicago.”

q represents the statement “It’s windy in Boston.”

Translate the following compound statement into words:

p q

A)

B)

C)

D)

8)

10)

It’s raining in Chicago and it’s windy in Boston.

It’s raining in Chicago or it’s windy in Boston.

It’s not the case that it’s raining in Chicago and windy in Boston.

If it’s raining in Chicago, it’s not windy in Boston.

Give the number of rows in the truth table for the compound statement.

11) (p q) (~r s) ~t

A) 32

B) 10

C) 8

Construct a truth table for the statement.

12) ~r ~s

A) r s (~r ~s)

T

T

F

F

C) r

T

F

T

F

s

F

F

F

F

(~r ~s)

T

T

F

F

T

F

T

F

F

F

F

T

D) 25

B) r s (~r ~s)

2

T

T

F

F

D) r

T

F

T

F

s

F

T

T

T

(~r ~s)

T

T

F

F

T

F

T

F

T

F

F

T

11)

12)

13) q ~p

A) q

p

q ~p

T

T

F

F

T

F

T

F

T

T

F

F

B) q

p

q ~p

T

T

F

F

T

F

T

F

F

T

T

T

C) q

p

q ~p

T

T

F

F

T

F

T

F

F

F

T

T

D) q

p

q ~p

T

T

F

F

T

F

T

F

T

F

T

T

13)

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound

statement.

14) (p ~q) r

14)

A) False

B) True

15) ~p (q ~r)

A) True

15)

B) False

Given p is true, q is true, and r is false, find the truth value of the statement.

16) ~r ~p

A) False

B) True

17) r

p

A) True

16)

17)

B) False

Tell whether the conditional statement is true or false.

18) Here F represents a false statement.

(2 = 2) F

A) True

18)

B) False

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound

statement.

19) p q

19)

A) True

B) False

20) p

20)

~q

A) False

B) True

Write a negation of the inequality. Do not use a slash symbol.

21) x < 4
A) x = 4
B) x > 4

C) x 4

Decide whether the statement is true or false.

22) Every rational number is an integer.

A) True

D) x < -4
B) False
Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
23) No turkeys like Thanksgiving.
A) If it is not a turkey, then it likes Thanksgiving.
B) If it is Thanksgiving, then turkeys like it.
C) If it is a turkey, then it doesn't like Thanksgiving.
D) If it is not Thanksgiving, then no turkeys like it.
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21)
22)
23)
Write an equivalent statement that does not use the if ... then connective. Use the fact that p
24) If the sun comes out Tuesday, the daisies will open.
A) The sun comes out Tuesday and the daisies will not open.
B) The sun does not come out Tuesday or the daisies will not open.
C) The sun does not come out Tuesday or the daisies will open.
D) The sun does not come out Tuesday but the daisies will not open.
q is equivalent to ~p v q.
24)
Let p represent 7 < 8, q represent 2 < 5 < 6, and r represent 3 < 2. Decide whether the statement is true or false.
25) (~p q) ~r
25)
A) True
B) False
4
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Tags:
compound statement
Converse
Contrapositive
De Morgans laws
negation of the conditional
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