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

Question

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 (A) B arrow( A ∨ C ) (B) (∼ B ) ∧( A ∧ C ) (C) B arrow((∼ A ) ∨(∼ C )) (D) B arrow( A ∧ C )

Tardigrade Admin · Accepted Answer

∼(( A ∧ C ) arrow B ) ∼(∼( A ∧ C ) ∨ B ) Using De-Morgan's law ( A ∧ C ) ∧(∼ B )

Q. 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

$B \to (A \lor C)$

$(\sim B) \land (A \land C)$

$B \to ((\sim A) \lor (\sim C))$

$B \to (A \land C)$

$\sim ((A \land C) \to B)$
$\sim (\sim (A \land C) \lor B)$
Using De-Morgan's law
$(A \land C) \land (\sim B)$

Q. 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

B→(A∨C)

(∼B)∧(A∧C)

B→((∼A)∨(∼C))

B→(A∧C)