Logical Equivalence Rules

Question 1

P V t = t and P ^ c = c

Answer 1

Universal Bound

Question 2

!(P V Q) = !P ^ !Q
or
!(P ^ Q) = !P V !Q

Answer 2

DeMorgan’s Law

Question 3

P ^ (Q ^ R) = (P ^ Q) ^ R

Answer 3

Associative

Question 4

(P -> Q) = !P V Q

Answer 4

Implication

Question 5

P ^ P = P or P V P = P

Answer 5

Idempotence

Question 6

P <-> Q = (P -> Q) ^ (Q-> P)

Answer 6

Biconditional Statement

Question 7

P -> Q = !Q -> !P

Answer 7

Contra positive

Question 8

!(P -> Q) = P ^ !Q

Answer 8

Negation of a conditional

Question 9

!(!P) = P

Answer 9

Double Negation

Question 10

P ^ t = P
or
P V c = P

Answer 10

Identity

Question 11

!t = c and !c = t

Answer 11

Negation of t and c

Question 12

P V !P = t and P ^ !P = c

Answer 12

Negation

Question 13

P ^ Q = Q ^ P

Answer 13

Commutative

Question 14

P ^ (Q V R) = (P ^ Q) V ( P ^ R)

P V (Q ^ R) = (P V Q) ^ (P V R)

Answer 14

Distributive

Question 15

P -> Q = ?

Answer 15

!P V Q (Implication)

Question 16

!(P -> Q) =

Answer 16

P ^ !Q (Negation of a conditional)

Question 17

What is the contra positive of !Q -> P?

Answer 17

!P -> Q

Question 18

!P ^ !Q = ?

Answer 18

!(P V Q) (DeMorgan’s Laws)

Question 19

P <-> Q = ?

Answer 19

(P -> Q) ^ (Q -> P) (Biconditional Statement)