Question

What is the contrapositive of the statement: if x=y then x²=y²

Answer 1

The contrapositive of the statement 'if x=y then x²=y²' is 'if x²≠y² then x≠y'.

Step-by-step explanation:

The contrapositive of the statement if x=y then x²=y² is: if x²≠y² then x≠y.

The contrapositive of a conditional statement switches the hypothesis and the conclusion and negates both. In this case, the original statement is if x=y then x²=y², so the contrapositive would be if x²≠y² then x≠y. This means that if two numbers have different squares, then those numbers themselves must be different.

For example, if x = 2 and y = 3, x² = 4 and y² = 9. Since x²≠y², the contrapositive statement x≠y is also true.