Question

The biconditional statement "x2 = 4 if and only if x = 2" is false. Split the statement into conditionals and determine which one(s) are incorrect. Explain why ?

Answer 1

The incorrect conditional statement is "If x = 2, then x² = 4." The statement "If x² = 4, then x = 2" is correct.

Step-by-step explanation:

The biconditional statement "x² = 4 if and only if x = 2" combines two conditional statements:

"If x = 2, then x² = 4."

"If x² = 4, then x = 2."

The first conditional statement is incorrect. For example, if x = -2, then x² = 4, but x is not equal to 2. Therefore, the statement "If x = 2, then x² = 4" is false.

The second conditional statement is correct. If x² = 4, then x can be either 2 or -2. Therefore, the statement "If x² = 4, then x = 2" is true.

In summary, the biconditional statement is false because the first conditional statement is incorrect. The correct interpretation is that if x equals 2, then x² equals 4, but if x² equals 4, x can be either 2 or -2. This highlights the importance of careful consideration in mathematical statements, particularly when dealing with squares and square roots.