prove this is a tautology?

Question

Show that this is a tautology without creating a truth table (changing logical expression)

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

nope I typed this correctly

this is not a union or set problem, the v means or and ^ means and -- > means imply. I am asked to proof this by the logical operator

Answer 1

The first term is all p and all q.
The second is no p and all r.

The intersection of all p and no p is nothing.
Therefore the only thing that will be in this intersection is about q and r.

However, I think it should be q ^ r, not q v r. Did you type it incorrectly?

Answer 2

Assume x does not lie within (q u r), then x is not in either q or r. Since x cannot be in both p and ~ p, and by assumption it is in neither q nor r, therefore x cannot lie within (p u q) and (~p u r).

Any x that is not within the right side is not within the left, therefore we have proven the tautology by proof of the contrapositive.

Answer 3

relies upon on what your classification ability by utilizing "instruct". in one case, you in basic terms could do a reality table and instruct that that assertion is often actual. In yet another, you may initiate with the regulation of the excluded center: P or notP Q or notQ and use the two certainly one of them to instruct that the assertion is actual.