Verified Solution • 2025–26 Session moderate

QJEEM19Ma51c0: JEE Main 2019 Mathematics - Class 11 JEEM19Ma51c0 Solution: If q is false and p q r is true, then which one of the…

If q is false and p ∧\wedge q ↔\leftrightarrow r is true, then which one of the following statements is a tautology ?

Multiple Choice Options

  • A P ∧\wedge r
  • B (p ∨\vee r) →\to (p ∧\wedge r)
  • C p ∨\vee r
  • D (p ∧\wedge r) →\to (p ∨\vee r)

Step-by-Step Verified Solution

Given q is F and (p ∧\wedge q) ↔\leftrightarrow r is T

⇒\Rightarrow   p ∧\wedge q is F which implies that r is F

⇒\Rightarrow   q is F and r is F

⇒\Rightarrow   (p ∧\wedge r) is always F

⇒\Rightarrow   (p ∧\wedge r) →\to (p ∨\vee r) is tautology.

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