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[16pt] Which of the following formulas are semantically equivalent to p → (q ∨ r): For...

  1. [16pt] Which of the following formulas are semantically equivalent to p → (q ∨ r): For each formula from the following (denoted by X) that is equivalent to p → (q ∨ r), prove the validity of X « p → (q ∨ r) using natural deduction. For each formula that is not equivalent to p → (q ∨ r), draw its truth table and clearly mark the entries that result in the inequivalence. Assume the binding priority used in class.

(2.1) q ∨ (¬p ∨ r)

(2.2) q ∧ ¬r → p

(2.3) p ∧ ¬r → q

(2.4) ¬q ∧ ¬r → ¬p

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Answer #1

(2.1)Given:

In row 4 and row6 both are not equal.

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