MHT CET202521 Apr 2025Morning ShiftMathematicsMathematical ReasoningActual
The logical statement [ ( p q ) ( p r ) ( q r )] is equivalent to
Options
- A(p r) q
- B( p q ) r
- Cp r
- D(p q) r
Correct answer
A. (p r) q
Step-by-step solution
The given statement is [ ( p q) (p r)] ( q r) . Applying De Morgan's law to ( p q) yields p q . Substituting gives [(p q) (p r)] ( q r) . The distributive law simplifies the disjunction to p ( q r) . The expression becomes p ( q r) ( q r) . Since ( q r) ( q r) q r , the entire expression reduces to p q r . This matches option A: (p r) q .