Verified Solution • 2025–26 Session moderate

QJEEM19Ma29a2: JEE Main 2019 Mathematics - Class 11 JEEM19Ma29a2 Solution: Which one of the following Boolean expressions is a tautology?

Which one of the following Boolean expressions is a tautology?

Multiple Choice Options

  • A (p ∨ q) ∧ (~ p ∨ ~ q)
  • B (p ∨ q) ∨ ( p ∨ ~ q)
  • C (p ∧ q) ∨ ( p ∧ ~ q)
  • D (p ∨ q) ∧ ( p ∨ ~ q)

Step-by-Step Verified Solution

(p ∨ q) ∨ (p ∨ ~ q)

= p ∨ (q ∨ p) ∨ ~ q

= (p ∨ p) ∨ (q ∨ ~ q)

= p ∨ T

= T so first statement is tautology

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