Verified Solution • 2025–26 Session moderate

QJEEM23Ma6171: JEE Main 2023 Mathematics - Class 11 JEEM23Ma6171 Solution: The negation of the expression is equivalent to

The negation of the expression q∨((∼ q)∧p)q \vee \left( {( \sim \,q) \wedge p} \right) is equivalent to

Multiple Choice Options

  • A (∼ p)∧(∼ q)( \sim \,p) \wedge ( \sim \,q)
  • B (∼ p)∨q( \sim \,p) \vee q
  • C p∧(∼ q)p \wedge ( \sim \,q)
  • D (∼ p)∨(∼ q)( \sim \,p) \vee ( \sim \,q)

Step-by-Step Verified Solution

q∨(∼q∧p)q \vee(\sim q \wedge p)

⇒(q∨∼q)∧(q∨p)\Rightarrow(q \vee \sim q) \wedge(q \vee p)

⇒T∧(q∨p)\Rightarrow T \wedge(q \vee p)

⇒q∨p\Rightarrow q \vee p

Now,

∼(q∨p)\sim(q \vee p)

=∼q∧∼p=\sim q \wedge \sim p

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