Verified Solution • 2025–26 Session moderate

QJEEM20Maf838: JEE Main 2020 Mathematics - Class 11 JEEM20Maf838 Solution: The negation of the Boolean expression p (~p q) is equivalent…

The negation of the Boolean expression p ∨\vee (~p ∧\wedge q) is equivalent to :

Multiple Choice Options

  • A p∧∼qp \wedge \sim q
  • B ∼\sim p∨∼qp \vee \sim q
  • C ∼p∧q\sim p \wedge q
  • D ∼p∧∼q\sim p \wedge \sim q

Step-by-Step Verified Solution

p ∨\vee (~p ∧\wedge q)

= (p ∨\vee ~p) ∧\wedge (p ∨\vee q)

= (T) ∧\wedge (p ∨\vee q)

= (p ∨\vee q)

Now negation of (p ∨\vee q) is

∼\sim (p ∨\vee q) = ∼p∧∼q\sim p \wedge \sim q

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