Proof that the following given propositions. 1. (p + r) A (q + r) = (p v q) +r 2. (p + q) v (p + r) = p + (q v r) 3. (p + r) v (q + r) = (p A q) + r 4. -(p + q) =p + -9 5. [- p A (p v q)] + q is a...

Proof that the following given propositions.

answer only 3, 4, and 6

Extracted text: Proof that the following given propositions. 1. (p + r) A (q + r) = (p v q) +r 2. (p + q) v (p + r) = p + (q v r) 3. (p + r) v (q + r) = (p A q) + r 4. -(p + q) =p + -9 5. [- p A (p v q)] + q is a tautology. 6. [(p + q)A (q + r)] + [p + r] is a tautology.