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Which of the following is logically equivalent to the proposition p → (q → p)?

1. p → (p → q)
2. p → (p ∨ q)
3. p → (p ∧ q)
4. p → (p ⇔ q)

Correct answer: p → (p ∨ q)

Solution

The proposition p → (q → p) asserts that if p is true, then regardless of the truth value of q, p remains true. This is logically equivalent to p → (p ∨ q), which states that if p is true, then at least one of p or q must be true, thus maintaining the truth of p.

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