Questions: 1. Test the following statement to see if it is reversible. If so, choose the true biconditional. If x=3, then x^2=9. x^2=9 if and only if x=3 This statement is not reversible. x=3 if and only if x^2=9. If x^2=9, then x=3

1. Test the following statement to see if it is reversible. If so, choose the true biconditional.

If x=3, then x^2=9.
x^2=9 if and only if x=3
This statement is not reversible.
x=3 if and only if x^2=9.
If x^2=9, then x=3

Transcript text: 1. Test the following statement to see if it is reversible. If so, choose the true biconditional. If $x=3$, then $x^{2}=9$. $x^{2}=9$ if and only if $x=3$ This statement is not reversible. $x=3$ if and only if $x^{2}=9$. If $x^{2}=9$, then $x=3$

Solution

Solution Steps

To determine if the statement "If $ x = 3 $, then $ x^2 = 9 $" is reversible, we need to check if the converse is true. The converse of the statement is "If $ x^2 = 9 $, then $ x = 3 $". If both the original statement and its converse are true, then the statement is reversible and we can form a true biconditional statement.

Solution Approach

Check if the original statement "If $ x = 3 $, then $ x^2 = 9 $" is true.
Check if the converse "If $ x^2 = 9 $, then $ x = 3 $" is true.
If both are true, the statement is reversible and we can form a biconditional statement.

Step 1: Verify the Original Statement

The original statement is "If $ x = 3 $, then $ x^2 = 9 $".

For $ x = 3 $: \[ x^2 = 3^2 = 9 \]

Thus, the original statement is true.

Step 2: Verify the Converse Statement

The converse statement is "If $ x^2 = 9 $, then $ x = 3 $".

For $ x^2 = 9 $: \[ x = \pm 3 \]

Thus, the converse statement is not always true because $ x $ can be either 3 or -3.

Step 3: Determine Reversibility

Since the converse statement is not always true, the original statement is not reversible.