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JEE Main 202124 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2021 · 24 February · Morning Shift · Mathematics · Mathematical Reasoning

The statement among the following that is a tautology is:

The statement among the following that is a tautology is:

Options

  1. AA∨(A∧B)A ∨ \left(A ∧ B\right)
  2. BA∧(A∨B)A ∧ \left(A ∨ B\right)
  3. CB→[A∧(A→B)]B \to \left[A ∧ \left(A \to B\right)\right]
  4. D[A∧(A→B)]→B\left[A ∧ \left(A \to B\right)\right] \to B

Correct answer

D. [A∧(A→B)]→B\left[A ∧ \left(A \to B\right)\right] \to B

Step-by-step solution

(A∧(A→B))→B\left(A ∧ \left(A \to B\right)\right) \to B

=(A∧( A∨B))→B= \left(A ∧ \left(~ A ∨ B\right)\right) \to B

=((A∧ A)∨(A∧B))→B= \left(\left(A ∧ ~ A\right) ∨ \left(A ∧ B\right)\right) \to B

=(A∧B)→B= \left(A ∧ B\right) \to B

= (A∧B)∨B= ~ \left(A ∧ B\right) ∨ B

=( A∨ B)∨B= \left(~ A ∨ ~ B\right) ∨ B

=T= T

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