prove-p-q-and-negetion-of-q-negation-of-p-

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