Verified Solution • 2025–26 Session moderate

QJEEM19Ma5e07: JEE Main 2019 Mathematics - Class 11 JEEM19Ma5e07 Solution: The Boolean expression ((p q) (p q)) ( p q) is equivalent to :

The Boolean expression ((p ∧\wedge q) ∨\vee (p ∨\vee ∼\sim q)) ∧\wedge ( ∼\sim p ∧\wedge ∼\sim q) is equivalent to :

Multiple Choice Options

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

Step-by-Step Verified Solution

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

≡\equiv (((p∨(p∨∼q)))∧(q∨(p∨∼q)))∧(∼p∧∼q)\left( {\left( {\left( {p \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( {q \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)

≡\equiv ((p∨∼q)∧(q∨∼q∨p))∧(∼p∧∼q)\left( {\left( {p \vee \sim q} \right) \wedge \left( {q \vee \sim q \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)

≡\equiv ((p∨∼q)∧(t∨p))∧(∼p∧∼q)\left( {\left( {p \vee \sim q} \right) \wedge \left( {t \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)

≡\equiv ((p∨∼q)∧t)∧(∼p∧∼q)\left( {\left( {p \vee \sim q} \right) \wedge t} \right) \wedge \left( { \sim p \wedge \sim q} \right)

≡\equiv (p∨∼q)∧(∼p∧∼q)\left( {p \vee \sim q} \right) \wedge \left( { \sim p \wedge \sim q} \right)

≡\equiv (p∧∼p∧∼q)∨(∼q∧∼p∧∼q)\left( {p \wedge \sim p \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p \wedge \sim q} \right)

≡\equiv (f∧∼q)∨(∼q∧∼p)\left( {f \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p} \right)

≡\equiv f′∨(∼q∧∼p)f' \vee \left( { \sim q \wedge \sim p} \right)

≡\equiv (∼q∧∼p)\left( { \sim q \wedge \sim p} \right)

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