NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice
If p and q are two logical statements, then p ⇒ q ⇒ p is equivalent to
Options
- Ap ⇒ p ⇒ q
- Bp ⇒ p ∨ q
- Cp ⇒ p ∧ q
- 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