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JEE Main202313 Apr 2023Morning ShiftMathematicsMathematical ReasoningActual

The negation of the statement ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A is

Options

  1. Aequivalent to ~ C
  2. Bequivalent to B ∨ ~ C
  3. Ca fallacy
  4. Dequivalent to ~ A

Correct answer

D. equivalent to ~ A

Step-by-step solution

Given, ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A We know that, X ⇒ Y ≡ ~ X ∨ Y , Now using the above formula we get, ≡ ~ ( A ∧ ( B ∨ C ) ) ∨ ( A ∨ B ) ⇒ A ≡ ~ ( ~ ( A ∧ ( B ∨ C ) ) ∨ ( A ∨ B ) ) ∨ A ≡ ( A ∧ ( B ∨ C ) ) ∧ ~ ( A ∨ B ) ∨ A Now to solve ( A ∧ ( B ∨ C ) ) ∧ ~ ( A ∨ B ) let us assume a universal set 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ,

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