Verified Solution • 2025–26 Session moderate

QJEEM21Mac499: JEE Main 2021 Mathematics - Class 11 JEEM21Mac499 Solution: Let F 1 (A, B, C) = (A B) [ C (A B)] A and F 2 (A, B) = (A B)…

Let F1(A, B, C) = (A ∧\wedge ∼\sim B) ∨\vee [ ∼\sim C ∧\wedge (A ∨\vee B)] ∨\vee ∼\sim A and
F2(A, B) = (A ∨\vee B) ∨\vee (B →\to ∼\sim A) be two logical expressions. Then :

Multiple Choice Options

  • A Both F1 and F2 are not tautologies
  • B F1 and F2 both are tautologies
  • C F1 is not a tautology but F2 is a tautology
  • D F1 is a tautology but F2 is not a tautology

Step-by-Step Verified Solution

Truth table for F1 :
JEE Main 2021 (Online) 26th February Evening Shift Mathematics - Mathematical Reasoning Question 66 English Explanation 1 ∴\therefore F1 is not a tautology.

Truth table for F2 :
JEE Main 2021 (Online) 26th February Evening Shift Mathematics - Mathematical Reasoning Question 66 English Explanation 2
∴\therefore F2 is a tautology.

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