Mathematical ReasoningHard

Question

Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement ″Suman is brilliant and dishonest if and only if Suman is rich″ can be expressed as

Options

A.~ (Q ↔ (P ~ R))
B.~ Q ↔ ~ P R
C.~ (P ~ R) ↔ Q
D.~ P (Q ↔ ~ R)

Solution

~ {(P ~ R ↔ Q} = ~ {Q ↔ ( P ~ R)}

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