Discrete Math Prove via the indirect method Please note tha

Discrete Math - Prove via the indirect method

Please note that the [comma-separated] hypotheses (to the left of the ==>).

Please note ^ means AND, v means or, <--> means biconditional, -> means if then/implies

A) r -> ~q , r v s , s -> ~q , p -> q => ~p

B) j , ~( a -> i ) -> ~ (j V e) , (i -> a) v ~j ==> a <-> i

C) s -> ~q , ~r <-> q , s v r , ~r ==> p
for c, p not beingmentioned in the hypothesis is a clue that the premises themselves are inconsistent.

Solution

A) s -> ~q negating this.

q->~s

p -> q we get p->s transitivity

rVs =r simplification

modus pones on r -> ~q we get ~q

applying modus pones on p -> q we get ~p.