Verified Solution • 2025–26 Session moderate

QJEEM22Ma9d11: JEE Main 2022 Mathematics - Class 11 JEEM22Ma9d11 Solution: is equivalent to when is

(p∧r)⇔(p∧(∼q))(p \wedge r) \Leftrightarrow(p \wedge(\sim q)) is equivalent to (∼p)(\sim p) when rr is

Multiple Choice Options

  • A pp
  • B ∼p\sim p
  • C qq
  • D ∼q\sim q

Step-by-Step Verified Solution

The truth table

p q ∼\sim p ∼\sim q p ∧\wedge q p ∧\wedge    ∼\sim q p ∧\wedge q ⇔\Leftrightarrow p ∧\wedge ∼\sim q
T T F F T F F
T F F T F T F
F T T F F F T
F F T T F F T

Clearly p ∧\wedge q ⇔\Leftrightarrow p ∧\wedge ∼\sim q ≡\equiv ∼\sim p

∴\therefore r = q

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