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If p and q are two statements, then which of the following statement is a tautology

Options

  1. Ap ⇒ p ∨ ~ q
  2. Bp ∨ q ⇒ p
  3. Cp ⇒ p ∧ q
  4. Dp ⇔ p ⇒ q

Correct answer

A. p ⇒ p ∨ ~ q

Step-by-step solution

p ⇒ p ∨ ~ q ≡ ~ p ∨ ( p ∨ ~ q ) ≡ ~ p ∨ p ∨ ~ q We know, ~ p ∨ p is always true i.e. the given statement is always true, hence, a tautology

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