Question

Q15. Without using truth table, prove that
[(p vq)^~p] →q is a tautology.​

Answer 1

Answer:

As you note, if QQ is true, then the implication is true.

And if QQ is false, we have that ¬P∧(P∨Q)≡(¬P∧P)F∨(¬P∧QF)FF¬P∧(P∨Q)≡(¬P∧P)⏟F∨(¬P∧Q⏟F)⏟F⏟F and any implication with a false premise is true.

Hence, the implication is a tautology.

Step-by-step explanation:

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