Use the theorems presented in this chapter to prove the foll

Use the theorems presented in this chapter to prove the following result. Cite the theorems used in each step (P vol R AS) is equivalent to P v R)A(ng v R) A( P v s A 0 S)

Solution

p ----> q

~p v q

q v ~p by 1.1 b

~(~q) v ~p

~ q--------> ~p.

b) p------>(q-------> r)

p--------> (~q v r)

~ p v (~ q v r)

(~p v~q) v r by 1.1 d

~( p ^ q) v r by 1.1 h

p ^ q ----------> r

c) p --------> (q ^ r)

~ p v (q ^ r) by 1.2

(~p v q) ^ (~p ^ r) by 1.1 g

(p --------> q )^ (p ----------> r) by 1.2