¬(p ⇒ q) and p ∧ ¬q

Question

Show that the following pairs of propositions are logically equivalent.

Answer 1

The given left side is

not (p --> q) =

not ( not p or q) = <-- Implication identity

p and not q <-- DeMorgan's Law

which is the right side

now by truth table

===========================================

p q ~q p->q left side right side

T T F T F F

T F T F T T

F T F T F F

F F T T F F