Verified Solution • 2025–26 Session moderate

QJEEM21Mad240: JEE Main 2021 Mathematics - Class 11 JEEM21Mad240 Solution: The statement (p (p q) (q r)) r is :

The statement (p ∧\wedge (p →\to q) ∧\wedge (q →\to r)) →\to r is :

Multiple Choice Options

  • A a tautology
  • B equivalent to p →\to ∼\sim r
  • C a fallacy
  • D equivalent to q →\to ∼\sim r

Step-by-Step Verified Solution

(p ∧\wedge (p →\to q) ∧\wedge (q →\to r)) →\to r

≡\equiv (p ∧\wedge ( ∼\sim p ∨\vee q) ∨\vee ( ∼\sim q ∨\vee r)) →\to r

≡\equiv ((p ∧\wedge q) ∧\wedge ( ∼\sim p ∨\vee r)) →\to r

≡\equiv (p ∧\wedge q ∧\wedge r) →\to r

≡\equiv ∼\sim (p ∧\wedge q ∧\wedge r) ∨\vee r

≡\equiv ( ∼\sim p) ∨\vee ( ∼\sim q) ∨\vee ( ∼\sim r) ∨\vee r

⇒\Rightarrow tautology

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