JEE Main202324 Jan 2023Evening ShiftMathematicsMathematical ReasoningActual
Let p and q be two statements. Then ~ ( p ∧ ( p → ~ q ) is equivalent to
Options
- Ap ∨ ( p ∧ ( ~ q ) )
- Bp ∨ ( ( ~ p ) ∧ q )
- C~ p ∨ q
- Dp ∨ ( p ∧ q )
Correct answer
C. ~ p ∨ q
Step-by-step solution
Given, ~ ( p ∧ ( p → ~ q ) ≡ ~ p ∨ ~ ( ~ p ∨ ~ q ) as   A → B ≡ ~ A ∨ B ≡ ~ p ∨ ( p ∧ q ) as   ~ A ∨ B ≡ ~ A ∧ ~ B ≡ ( ~ p ∨ p ) ∧ ( ~ p ∨ q ) ≡ t ∧ ( ~ p ∨ q ) ≡ ~ p ∨ q ≡ ( ~ p ) ∨ q