Name: Answer Key
Date: ______ Class: ______
Logic Review Sheet
Ms. Anderle
Logic Review Sheet
Multiple Choice:
1) What is logically equivalent to ~q p?
a)~p q
b) p ~q
c) q  ~p
2) What is the converse of t r?
a) ~t ~r
b) ~r  ~t
c) r  t
3) What is the inverse of w  ~v?
a) v  ~w
b) ~w  v
c) ~v  w
4) What is the converse of the statement, “If it is Monday, then I am watching Gossip Girl”?
a) If it is not Monday, then I am not watching Gossip Girl.
b) If I am not watching Gossip Girl, then it is not Monday.
c) If I am watching Gossip Girl, then it is Monday.
d) If I am watching Gossip Girl, then it is not Monday.
5) Which statement is logically equivalent to “If it is snowing, then I am wearing a scarf”?
a) If it is not snowing, then I am not wearing a scarf.
b) If I am not wearing a scarf, then it is not snowing.
c) If I am wearing a scarf, then it is snowing.
d) It is snowing if and only if I am wearing a scarf.
6) The statement “Patrick plays on the football team or Patrick bakes cookies” is false. Which
statement is true?
a) Patrick does not play on the football team and Patrick does not bake cookies.
b) Patrick plays on the football team and Patrick bakes cookies.
c) Patrick does not play on the football team and Patrick bakes cookies.
d) Patrick plays on the football team and Patrick does not bake cookies.
7) A conditional statement is always logically equivalent to its
a) Inverse
b) Conjunction
c) Contrapositive
d) Converse
Write the converse, inverse, and contrapositive of the given conditional:
1) “If I watch Friends, then I am happy.”
Converse: If I am happy, then I am watching Friends.
Inverse: If I am not watching Friends, then I am not happy.
Contrapositive: If I am not happy, then I am not watching Friends.
Which ones is logically equivalent to the original statement? contrapositive
For the questions below use the following statements:
Let p represent: Friends was a TV show.
Let q represent: Gossip Girl is on Tuesday nights.
Let r represent: A dog is not an animal.
Let s represent: All triangles have four sides.
1) Translate each statement into symbolic form:
a) Friends was not a TV show.
~p__
b) If Gossip Girl is not on Tuesday nights, then all triangles have four sides.
~q  s
c) Friends was a TV show if and only if Gossip Girl is not on Tuesday nights.
p ~q
d) All triangles have four sides or a dog is not an animal.
sVr
2) Determine the truth value of the statements below:
a) ~r  s
False
b) s  r
True
c) r V q
False
d) ~p ^ ~r
False
Label each statement as true, false, or open:
1) Hawaii is not an island.
False
2) Her cat is yellow.
Open
3) All apples are vegetables.
False
4) Massapequa is on Long Island.
True
5) My hair is green.
Open
Write the negation of each statement:
1) Purple is my favorite color.
Purple is not my favorite color.
2) Venus is not the second planet from the sun.
Venus is the second planet from the sun.
3) The sky is blue.
The sky is blue.
4) 3 + 4 = 8
3+4≠8
Construct a truth table for a conjunction, disjunction, conditional, and biconditional.
Conjunction:
Disjunction:
p
q
p^q
p
q
pVq
T
T
T
T
T
T
T
F
F
T
F
T
F
T
F
F
T
T
F
F
F
F
F
F
Conditional:
Biconditional:
p
q
pq
T
T
T
T
F
F
F
T
T
F
F
T
p
q
p  q
T
T
T
T
F
F
F
T
F
F
F
T
Are these statements logically equivalent? Why or why not?
pq
~p V q
p
T
T
F
F
q
T
F
T
F
~p
F
F
T
T
~pVq
T
F
T
T
p→q
T
F
T
T
(p → q)  (~ p V q)
T
T
T
T
Yes, these statements are logically equivalent. Because the biconditional of the these two
statements is a tautology (the last column is all true).