Consider the following statements: P : Suman is brilliant Q : Suman is rich R : Suman is honestThe negation of the statement "Suman is brilliant and d - Mathematics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

The given statement is: (P \land \sim R) \leftrightarrow Q .The negation of a biconditional A \leftrightarrow B is logically equivalent to \sim A \leftrightarrow B or A \leftrightarrow\sim B .Therefore, the negation is \sim (P \land \sim R) \leftrightarrow Q, which is (\sim P \lor R) \leftrightarrow Q .Alternatively, it can be written as (P \land \sim R) \leftrightarrow\sim Q .From the options, \sim Q \leftrightarrow (P \land \sim R) matches the logical form A \leftrightarrow\sim B .

Try it yourself before checking the explanation above.

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

\sim Q \leftrightarrow (P \land \sim R)

\sim Q \leftrightarrow (\sim P \land R)

(\sim P \land \sim R) \leftrightarrow Q

(\sim P \land Q) \leftrightarrow\sim R

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