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  • Consider the following statements : Suman is brilliant <img alt="Q" src="https://learn.careers

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

Option: 1

\sim Q\leftrightarrow \sim P\wedge R\;


Option: 2

\; \sim (P\wedge \sim R)\leftrightarrow Q\;


Option: 3

\; \; \sim P\wedge (Q\leftrightarrow \sim R)\; \;


Option: 4

\; \sim (Q\leftrightarrow (P\wedge \sim R))


Answers (1)

best_answer
 

Algebra of Statements -

-

 Given statement is

(P\wedge \sim R) \leftrightarrow Q

which is same as

Q \leftrightarrow (P\wedge \sim R)

Since it is a biconditional statement

Hence negation is 

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

Posted by

mansi

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