Verified Solution • 2025–26 Session moderate

QJEEM21Mae78a: JEE Main 2021 Mathematics - Class 11 JEEM21Mae78a Solution: The statement among the following that is a tautology is :

The statement among the following that is a tautology is :

Multiple Choice Options

  • A B→[A∧(A→B)]B \to \left[ {A \wedge \left( {A \to B} \right)} \right]
  • B [A∧(A→B)]→B\left[ {A \wedge \left( {A \to B} \right)} \right] \to B
  • C [A∧(A∨B)]\left[ {A \wedge \left( {A \vee B} \right)} \right]
  • D [A∨(A∧B)]\left[ {A \vee \left( {A \wedge B} \right)} \right]

Step-by-Step Verified Solution

Given, [A∧(A→B)]→B\left[ {A \wedge \left( {A \to B} \right)} \right] \to B

= A∧(∼A∨B)→BA \wedge \left( { \sim A \vee B} \right) \to B

= [(A∧∼A)∨(A∧B)]→B\left[ {\left( {A \wedge \sim A} \right) \vee \left( {A \wedge B} \right)} \right] \to B

= (A∧B)→B\left( {A \wedge B} \right) \to B

= ∼A∨∼B∨B{ \sim A \vee \sim B \vee B}

= t

Hence, [A∧(A→B)]→B\left[ {A \wedge \left( {A \to B} \right)} \right] \to B is a tautology.

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