Exam study guide

Exam
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
1) ~(p ∧ q), ~p ∧ ~q
A) Not equivalent
B) Equivalent
2) ~(p ∨ q) , ~p ∧ ~q
A) Equivalent

B) Not equivalent

3) (p ∨ q) ∨ r, p ∨ (q ∨ r)
A) Not equivalent

1)

B) Equivalent

2)

3)

Write an equivalent sentence for the statement.
4) It is not true that you are a day late and a dollar short. (Hint: Use De Morganʹs laws.)
A) You are not a day late and a dollar short.
B) You are a day late or not a dollar short.
C) You are not a day late or not a dollar short.
D) You are not a day late and not a dollar short.
5) Denim is not out and linen is not in. (Hint: Use De Morganʹs laws.)
A) Denim and linen are in.
B) It is not the case that denim is out or linen is in.
C) It is not the case that denim is out and linen is in.
D) It is not the case that denim is in or linen is out.
Write the indicated statement. Use De Morgan’s Laws if necessary.
6) If I pass, Iʹll party.
Contrapositive
A) If I donʹt party, I didnʹt pass.
C) If I donʹt pass, I wonʹt party.

4)

5)

6)

B) If I party, then I passed.
D) Iʹll party if I pass.

7) If it is a cat, then it catches birds.

7)

Inverse
A) If it doesnʹt catch birds, itʹs not a cat.
C) Not all cats catch birds.

B) If it catches birds, itʹs a cat.
D) If itʹs not a cat, it doesnʹt catch birds.

8) If it is love, then it is blind.

8)

Contrapositive
A) If it is blind then it is not love.
C) If it is blind then it is love.

B) If it is not blind, then it is not love.
D) It is blind if it is love.

1

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false.
9)
9) If the triangle is not equilateral, then the three sides of the triangle are not equal.