prove p⇒q and negetion of q⇒negation of p


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Question Number 78671 by berket last updated on 19/Jan/20

$p r o v e p \Rightarrow q a n d n e g e t i o n o f q \Rightarrow n e g a t i o n o f p$
	Answered by Rio Michael last updated on 19/Jan/20

	$t o p r o v e t h a t p \Rightarrow q \equiv q \Rightarrow\sim p$ $1 s e t u p a t r u t h t a b l e$ $p q \sim p \sim q p \Rightarrow q \sim q \Rightarrow\sim p$ $T T F F T T$ $T F F T F F$ $F T T F T T$ $F F T T T T$ $w e s e e t h a t t h e l a s t c o l u m n s a r e t h e r e s a m e$ $t h u s p \Rightarrow q \equiv \sim q \Rightarrow\sim p$ $2 U s i n g D^{'} m o r g a n s l a w$ $p \Rightarrow q \equiv \sim (p \Leftarrow q)$ $\equiv \sim q \Rightarrow \sim p$ $a l s o \sim q \Rightarrow\sim p \equiv \sim (q \Leftarrow p)$ $\equiv p \Rightarrow q$ $h e n c e t h e y a r e c o r r e c t$
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