Question

Test the conditional statement and its converse to determine whether the following biconditional is true.


x3 = 125 if and only if x = 5.


A.
It is true because at least one part of the biconditional is true.


B.
It is true because both parts of the biconditional are true.


C.
It is false because both parts of the biconditional are false.


D.
It is false because at least one part of the biconditional is false.

Answer 1

D. It is false because at least one part of the biconditional is false.

If x = 5, then x^3 = 125 (since 5^3 = 125). However, if x^3 = 125, it does not necessarily mean that x = 5, as there are other numbers whose cube is also 125 (for example, -5). Thus, the original biconditional statement is false.