MHT CET202616 April 2026Evening ShiftMathematicsMathematical ReasoningActual
The negation of the contrapositive of the statement (p q) (p q) is
Options
- A(p q) ( p q)
- B( p q) (p q)
- C( p q) (p q)
- D( p q) (p q)
Correct answer
D. ( p q) (p q)
Step-by-step solution
The contrapositive of a conditional statement X Y is logically equivalent to the statement itself. Therefore, the negation of the contrapositive of X Y is logically equivalent to the negation of X Y . The negation of X Y is X Y . Given the statement (p q) (p q) , we have X = p q and Y = p q . The negation of the statement is: X Y = (p q) (p q) By De Morgan's laws, (p q) p q . Substituting this back, we get: (p q) ( p q) Rearranging the terms, this is identical to ( p q) (p q) .