Verified Solution • 2025–26 Session moderate

QJEEM20Ma9bbd: JEE Main 2020 Mathematics - Class 11 JEEM20Ma9bbd Solution: Which of the following is a tautology ?

Which of the following is a tautology ?

Multiple Choice Options

  • A (∼p)∧(p∨q)→q\left( { \sim p} \right) \wedge \left( {p \vee q} \right) \to q
  • B (q→p)∨∼(p→q)\left( {q \to p} \right) \vee \sim \left( {p \to q} \right)
  • C (p→q)∧(q→p)\left( {p \to q} \right) \wedge \left( {q \to p} \right)
  • D (∼q)∨(p∧q)→q\left( { \sim q} \right) \vee \left( {p \wedge q} \right) \to q

Step-by-Step Verified Solution

~ p ∧\wedge (p ∨\vee q) →\to q

≡\equiv (~ p ∧\wedge p) ∨\vee (~ p ∧\wedge q) →\to q

≡\equiv C ∨\vee (~ p ∧\wedge q) →\to q    [C = contradiction]

≡\equiv (~ p ∧\wedge q) →\to q

≡\equiv ~ (~ p ∧\wedge q) ∨\vee q

≡\equiv (p ∨\vee ~ q) ∨\vee q

≡\equiv (p ∨\vee q) ∨\vee (~ q ∨\vee q)

≡\equiv (p ∨\vee q) ∨\vee t

so ~ p ∧\wedge (p ∨\vee q) →\to q is a tautology

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