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NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice

If p and q are two logical statements, then p ⇒ q ⇒ p is equivalent to

Options

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

Correct answer

B. p ⇒ p ∨ q

Step-by-step solution

p ⇒ q ⇒ p ≡ ~ p ∨ ~ q ∨ p ≡ ~ p ∨ p ∨ ~ q   ≡ t ∨ ~ q   ≡ t hence, p ⇒ q ⇒ p is a tautology Now, p ⇒ p ⇒ q is false when p is true and q is false p ⇒ q ∨ p   ≡ ~ p ∨ p ∨ q ≡ ~ p ∨ p ∨ q t ∨ q   ≡ t Hence, B is correct. Also, p ⇒ p ∧ q is false when p is true and q is false Also, p ⇒ p ⇔ q is false when p is true and q is

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