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For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.


If x = 9, then x2 = 81.


a)If x2 = 81, then x = 9.

b)If x2 = 81, then x = 9.

x2 = 81 if and only if x = 9.

c)If x2 = 9, then x = 81.

d)If x2 = 81, then x = 9.

x = 9 if and only if x2 = 81

Verified Answer :

Nirina7

x2 = 81 if and only if x = 9.
this statement means 

x2 = 81 implies x = 9, and x = 9 implies x²=81
 so the converse of If x = 9, then x2 = 81 is If x2 = 81, then x = 9

The converse statement  interchange the hypothesis and the conclusion.

The converse of x=9 then \(x^{2} =81.\)  is \(x^{2} = 81 then x=9.\) is true.

A biconditional statement is defined to be true whenever both parts have the same truth value . combining  the statements as a biconditional we have

If \(x^{2}\). = 81, then x = 9.  

x = 9 if and only if \(x^{2} .\) = 81

Option D is the right answer.

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