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 x^2 = 81
Converse: If x^2 = 81, then x = 9.
Biconditional: x = 9 if and only if x^2 = 81.
The given true conditional statement is: "If x = 9, then x^2 = 81."
To find the converse of this statement, we need to switch the hypothesis and conclusion. So the converse is: "If x^2 = 81, then x = 9."
To determine if the converse is also true, we can substitute values that satisfy the converse statement. Let's use x = 3 to test it:
If x^2 = 81, then (3)^2 = 81
9 = 81
Since this statement is false, the converse is not true.
Since the converse is not true, we cannot combine the original statement and its converse as a biconditional statement.
The given true conditional statement is: "If x = 9, then x^2 = 81."
To write the converse of this conditional statement, we simply interchange the "if" part and the "then" part.
Converse: "If x^2 = 81, then x = 9."
Now, in order to determine if the converse is also true, we need to substitute the values from the original statement into the converse and check if it holds.
Using x = 9, the converse becomes: "If 81 = 81, then 9 = 9."
Since the statement "81 = 81" is true, and "9 = 9" is also true, we can conclude that the converse is true.
To combine the original statement and the converse as a biconditional, we join the two statements using the phrase "if and only if."
Biconditional: "x = 9 if and only if x^2 = 81."
This means that x is equal to 9 if and only if x^2 is equal to 81. Both conditions must be true for the biconditional statement to hold.