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JEE Main202224 Jun 2022Evening ShiftMathematicsMathematical ReasoningActual

Consider the following statements: A : Rishi is a judge. B : Rishi is honest. C : Rishi is not arrogant. The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

Options

  1. AB → A ∨ C
  2. B~ B ∧ A ∧ C
  3. CB → ~ A ∨ ~ C
  4. DB → A ∧ C

Correct answer

B. ~ B ∧ A ∧ C

Step-by-step solution

if Rishi is a judge and he is not arrogant, then he is honest can be written as A ∧ C → B Now, Negation of A ∧ C → B is ~ A ∧ C → B = ~ ~ A ∧ C ∨ B Using De-Morgan's law = A ∧ C ∧ ~ B

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