Logical Equivalences

Question 1

Identity Laws

Answer 1

p ^ T = p

p v F = p

Question 2

Domination Laws

Answer 2

p v T = T

p ^ F = F

Question 3

Idempotent Laws

Answer 3

p v p = p

p ^ p = p

Question 4

Double negation law

Answer 4

¬(¬p) = p

Question 5

Commutative laws

Answer 5

p v q = p v q

p ^ q = q ^ p

Question 6

Associative laws

Answer 6

(p v q) v r = p v (q v r)

p ^ q) ^ r = p ^ (q ^ r

Question 7

Distributive laws

Answer 7

p v (q ^ r) = (p v q)^(p v r)
p ^ (q v r) = (p ^ q)v(p ^ r)

Question 8

De Morgan’s laws

Answer 8

¬(p ^ q) = ¬p v ¬q

¬(p v q) = ¬p ^ ¬q

Question 9

Absorption laws

Answer 9

p v (p ^ q) = p
p ^ (p v q) = p

Question 10

Negation laws

Answer 10

p v ¬p = T

p ^ ¬p = F