Prove the following statement: a bi-implication is true if and only if the hypothesis and the conclusion have the same truth value, i.e., use propositional logic (NOT TRUTH TABLE) to prove:

1) p q (p q) (p q)

2) e (s m) (s e) (m e) (s m e)

NOT TRUTH TABLE

USE PROPOSITIONAL LAWS

EXAMPLE:

p r) (q r) (p r) (q r) Conditional Identity

(p r) (q r) Conditional Identity

p (r (q r)) Associative law

p ((r q) r) Associative law

p ((q r) r) Commutative law

p (q (r r)) Associative law

p (q r) Idempotent law

(p q) r Associative law

(p q) r De Morgans law

(p q) r Conditional Identity