MHT CET202615 April 2026Morning ShiftMathematicsMathematical ReasoningActual
The dual of the converse of the inverse of the logical statement p (q r) is equivalent to...
Options
- A[p (r q)]
- Bp (r q)
- C[p (q r)]
- Dp (q r)
Correct answer
A. [p (r q)]
Step-by-step solution
The given statement is p (q r) . The inverse of a conditional statement A B is A B . The converse of C D is D C . Thus, the converse of the inverse of A B is B A , which is the contrapositive of the original statement. For p (q r) , the converse of the inverse is: (q r) p We can simplify this using the equivalence X Y X Y : (q r) p (q r) p ( q r) p p q r To find the dual of a logical expression, we replace with and with (while keeping the literals unchanged). The dual of ( p q r) is ( p q r) . Now, we check the giv