laws of propositional logic

Question 1

what are the idempotent laws?

Answer 1

p v p ≡ p

p ^ p ≡ p

Question 2

what are the associative laws?

Answer 2

p v (q v r) ≡ (p v q) v r

p ^ (q ^ r) ≡ (p ^ q) ^ r

Question 3

what are the commutative laws?

Answer 3

p v q ≡ q v p

p ^ q ≡ q ^ p

Question 4

what are the distributive laws?

Answer 4

p v (q ^ r) ≡ (p v q) ^ (p v r)

p ^ (q v r) ≡ (p ^ q) v (p ^ r)

Question 5

what are the identity laws?

Answer 5

p v F ≡ p

p ^ T = p

Question 6

what are the domination laws?

Answer 6

p v T ≡ T

p ^ F ≡ F

Question 7

what is the double negation law?

Answer 7

¬(¬p) ≡ p

Question 8

what are the complement laws?

Answer 8

p ^ ¬p ≡ F

p v ¬p ≡ T

Question 9

what are DeMorgan’s laws?

Answer 9

¬(p v q) ≡ ¬p ^ ¬q

¬(p ^ q) ≡ ¬p v ¬q

Question 10

what are the absorption laws?

Answer 10

p v (p ^ q) ≡ p

p ^ (p v q) ≡ p

Question 11

what are the conditional identities?

Answer 11

p –> q ≡ ¬p v q

p <–> q ≡ (p –> q) ^ (q –>p)