Question

. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 8, then x2 = 64.

Answer 1

Answer: The converse of the statement will be :

$\text{If }x^2 = 64\text{, then } x=8.$ which is not true.

Step-by-step explanation:

The given statement : $\text{If } x = 8\text{, then }x^2 = 64.$

To write a converse of a conditional statement "p then q",  will be "q then p" the hypothesis and conclusion interchanges .

Then the converse of the statement will be :

$\text{If } x^2 = 64\text{, then }x=8.$ which is not true.

Since , $8^2=64\text{ and }-8^2=64$

Therefore,  $\text{If }x^2 = 64\text{, then } x=8\ or\ x=-8.$

Answer 2

Answer:

If $x^2=64$, then x=8

Step-by-step explanation:

We are given that a conditional statement

If x=8, then $x^2=64$

if conditional statement

$P\implies Q$

Then, converse statement

$Q\implies P$

Converse statement of given conditional statement:

If $x^2=64$, then x=8

But , it is not true because when $x^2=64$, then $x=\pm 8$

Therefore, it is false.