Laws And Identities

Question 1

What are the identity laws?

Answer 1

P ^ 1 = P
P v 0 = P

Question 2

What are the domination laws?

Answer 2

1) P v 1 = 1
2) P ^ 0 = 0

Question 3

What are the idempotence laws

Answer 3

1) P ^ P = P
2) P v P = P

Question 4

What are the negation laws?

Answer 4

1) P ^ ~P = 0
2) P v ~ P = 1

Question 5

What is the double negation law?

Answer 5

~(~P) = P

Question 6

What are the commutative laws?

Answer 6

1) P ^ Q = Q ^ P
2) P v Q = Q v P

Question 7

What are the associative laws?

Answer 7

1) (P ^ Q) ^ S = P ^ (Q ^ S)
2) (P v Q) v S = P v ( Q v S)

Question 8

What are DeMorgan’s laws?

Answer 8

1) ~(P ^ Q) = (~P v ~ Q)
2) ~P v ~Q = ~(P ^ Q)

Question 9

What are the absorption laws?

Answer 9

1) P ^ (P v Q) = P
2) P v ( P ^ Q) = P

Question 10

What are the distributive laws for the following?
1) P ^ (Q v S)
2) P v (Q ^ S)

Answer 10

1) (P ^ Q) v (P ^ S)
2) (P v Q) ^ (P v S)

Question 11

What are the biconditional laws for the following?
1) P <==> Q
2) P => Q
3) P => Q

Answer 11

1) (P => Q) ^ ( Q => P)
2) (~Q => ~P)
3) ~P v Q