Simplifying Statement Forms
ANSWER:
Starting with the left hand side, replace portions of the expression with equivalent expressions until it has been reduced to p. (Each section to be replaced is highlighted.)
(p (~(~p q))) (p q) (p (~~p ~q)) (p q) | by DeMorgan's Laws |
(p (~~p ~ q)) (p q) (p (p ~q)) (p q) | by Double Negative Law |
(p (p ~q)) (p q) ((p p )~q) (p q) | by Associative Law |
((p p )~q) (p q) (p ~q) (p q) | by Idempotent Law |
(p ~q) (p q) p (~q q) | by Distributive Law |
p (~q q)p t | by Negation Laws |
p tp | by Identity Laws |