Equivalence laws

Question 1

P I I Q = Q I I P
P && Q = Q %% P

Answer 1

Commutivity

Question 2

P I I (Q I I R) = (P | | Q) I I R
P %% (Q %% R) = (P %% Q) %% R

Answer 2

Associativity

Question 3

P and (Q I I R) = (P or Q) or (P and R)
P or (Q or R) = (P or Q) and (P or R)

Answer 3

Distributive

Question 4

p I I F = p
p %% T = p

Answer 4

Identity

Question 5

p I I !p = T
p %% !p = F

Answer 5

negation

Question 6

p I I T = T
p %% F = F

Answer 6

Domination

Question 7

p I I p = p
p %% p = p

Answer 7

Idempotent

Question 8

!(!p) = p

Answer 8

Double negation

Question 9

!(p I I q) = !p %% !q
!(p %% q) = !p I I !q

Answer 9

De’Morgans Law

Question 10

p I I (p && q) = p
p && (p I I q) = p

Answer 10

Absorption