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JEE Main 202229 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Morning Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2022 · 29 June · Morning Shift · Mathematics · Mathematical Reasoning

Let Δ ∈ \ ∧ , ∨ , ⇒ , ⇔\ be such that (p ∧ q)Δ ((p ∨ q) ⇒ q) is a...

Let Δ∈{∧,∨,⇒,⇔}\Delta \in \left\{∧ , ∨ , ⇒ , ⇔\right\} be such that \left(p ∧ q\right)\Delta((p∨q)⇒q)\left(\left(p ∨ q\right) ⇒ q\right) is a tautology. Then Δ\Delta is equal to

Options

  1. A∧∧
  2. B∨∨
  3. C⇒⇒
  4. D⇔⇔

Correct answer

C. ⇒⇒

Step-by-step solution

p ∨ q ⇒ q</p><p></p><p>≡ ~ \left(p ∨ q\right) ∨ q</p><p></p><p>≡ \left(~ p ∧ ~ q\right) ∨ q</p><p></p><p>≡ \left(~ p ∨ q\right) ∧ \left(~ q ∨ q\right)</p><p></p><p>≡ \left(~ p ∨ q\right) ∧ t ≡ ~ p ∨ q</p><p>Now,</p><p>(p∧q)⇒ p∨q</p><p>Now, </p><p>\left(p ∧ q\right) ⇒ ~ p ∨ q

≡ p∨ q∨ p∨q≡ ~ p ∨ ~ q ∨ ~ p ∨ q

≡t≡ t

Hence, △△ should be ⇒⇒

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