Please help with this question!!!

Question

Show that the compound propositions   is a tautology using propositional laws.

Answer 1

~p and (p v q) =

(~p and p) v (~p and q) =

F v (~p and q) =

~p and q

Then the original statement is equal to:

(~p and q) --> q

Implication identity:

~(~p and q) v q

DeMorgan's:

(p v ~q) v q

Associative:

p v ( ~q v q)

p v True

True

Tautology proven

p q ~p p v q ~p and (p v q) final

T T F T F T

T F F T F T

F T T T T T

F F T F F T