Logic Laws

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

Negation Laws

Answer 3

p v ~p = T

p ^ ~p = F

Question 4

Associative Laws

Answer 4

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

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

Question 5

Commutative Laws

Answer 5

p v q = q v p

p ^ q = q ^ p

Question 6

DeMorgan’s Laws

Answer 6

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

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

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

Double Negation Law

Answer 8

~(~p ) = p

Question 9

Absorption Laws

Answer 9

p ^ (p v q) = p

p v ( p ^ q) = p

Question 10

Idempotent Law

Answer 10

p v p = p

p ^ p = p