Truth Tables & Logic Review
Name: __________________________________

You must complete this entire packet and turn in to substitute before the end of class.

You do NOT have homework, the homework on the syllabus for tonight has been included in
this packet (pg. 546-547 #1-5) so if you complete and turn in this packet you have done it.
1) Given the two statements, answer the following:
P: I do my homework
Q: I will get a good grade in math class
Write the Implication Statement (if…then): ____________________________________________________
__________________________________________________________________________________________________
Write the Converse: _______________________________________________________________________
__________________________________________________________________________________________
Write the Inverse: _______________________________________________________________________
__________________________________________________________________________________________
Write the Contrapositve: ___________________________________________________________________
__________________________________________________________________________________________
2) Construct Truth Tables for the following statements:
a)
p ⇒ ¬q
b)
¬q ⇒ ¬p
c)
q ˄ (p ⇒ q)
d) p
e) p ⇒ (p ˄ ¬q)
p
q
¬q
⇔ ¬q
f) (p ⇒ q) ⇒ ¬p
p ˄ ¬q
p ⇒ (p ˄ ¬q)
p
q
¬p
p ⇒ q (p ⇒ q) ⇒ ¬p
3) Show that each of the statements are equal (that means set up two separate truth tables, one for
the left hand side of equal sign and one for the right hand side) by comparing the last column of each.
a) p ⊻ q = ¬(p ⇔ q)
p
q
p⊻q
p
q
p⇔q
¬(p ⇔ q)
b) ¬p ⇒ q = p ˅ q
p
q
¬p
¬p ⇒ q
p
q
p˅q
p
q
p˄q
c) q ⇒ (p ⊻ q) = ¬(p ˄ q)
q
p⊻q
q ⇒ (p ⊻ q)
4) Write the converse and inverse for:
a) If Nicole is wearing a jumper, then she is warm.
Converse:
Inverse:
b) If two triangles are similar, then they are equiangular
Converse:
Inverse:
c) If 2x2 = 12, then x = ±√6
Converse:
Inverse:
¬(p ˄ q)
d) If Alex is in the playground, then he is having fun.
Converse:
Inverse:
e) If a triangle is equilateral, then its three sides are equal in length.
Converse:
Inverse: