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JEE Main202329 Jan 2023Evening ShiftMathematicsMathematical ReasoningActual

The statement B ⇒ ~ A ∨ B is not equivalent to :

Options

  1. AB ⇒ A ⇒ B
  2. BA ⇒ A ⇔ B
  3. CA ⇒ ~ A ⇒ B
  4. DB ⇒ ~ A ⇒ B

Correct answer

B. A ⇒ A ⇔ B

Step-by-step solution

Given statement is B ⇒ ~ A ∨ B Truth table for given statement: A B ~ A ~ A ∨ B B ⇒ ~ A ∨ B T T F T T T F F F T F T T T T F F T T T It is a tautology. Truth table of given options: A ⇒ B ~ A ⇒ B B ⇒ A ⇒ B A ⇒ ~ A ⇒ B B ⇒ ~ A ⇒ B T T T T T F T T T T T T T T T T F T T T Option A: B ⇒ A ⇒ B is a tautology. Option C: A ⇒ ~ A ⇒ B is a tautology. Option D: B ⇒ ~ A ⇒ B is a tautology. Hence, it is very clear t

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