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

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.

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

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.

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

Final Answer