Verified Solution • 2025–26 Session moderate

QJEEM21Made43: JEE Main 2021 Mathematics - Class 11 JEEM21Made43 Solution: Consider the two statements : (S1) : (p → q) ∨ ( ∼ q → p) is a…

Consider the two statements :

(S1) : (p → q) ∨ (∼ q → p) is a tautology .

(S2) : (p ∧ ∼ q) ∧ (∼ p ∧ q) is a fallacy.

Then :

Multiple Choice Options

  • A only (S1) is true.
  • B both (S1) and (S2) are false.
  • C both (S1) and (S2) are true.
  • D only (S2) is true.

Step-by-Step Verified Solution

S1 : (∼ p ∨ q) ∨ (q ∨ p) = (q ∨ ∼ p) ∨ (q ∨ p)

S1 = q ∨ (∼ p ∨ p) = qvt = t = tautology

S2 : (p ∧ ∼ q) ∧ (∼ p ∨ q) = (p ∧ ∼ q) ∧ ∼ (p ∧ ∼ q) = C = fallacy

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