JEE Main202313 Apr 2023Evening ShiftMathematicsMathematical ReasoningActual
The statement ( p ∧ ( ~ q ) ) ∨ ( ( ~ p ) ∧ q ) ∨ ( ( ~ p ) ∧ ( ~ q ) ) is equivalent to _ _ _ _ _
Options
- A~ p ∨ q
- B~ p ∨ ~ q
- Cp ∨ ~ q
- Dp ∨ q
Correct answer
B. ~ p ∨ ~ q
Step-by-step solution
Given, ( p ∧ ( ~ q ) ) ∨ ( ( ~ p )   ∧   q )   ∨ ( ( ~ p )   ∧   ( ~ q ) ) = ( ( ~ p )   ∧   q )   ∨ ( ( ~ p )   ∧   ( ~ q ) ) ∨ ( p ∧ ( ~ q ) ) = ~ p ∧ q ∨ ~ q ∨ p ∧ ~ q We know that ~ A ∨ A = T , where T is tautology, = ~ p ∧ T ∨ p ∧ ~ q = ~ p ∨ p ∧ ~ q = ~ p ∨ p ∧ ~ p ∨ ~ q = T ∧ ~ p ∨ ~ q = ~ p ∨ ~ q