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Answer 1

Answer:

If x^2=y^2, x is not always equal to y so that statement would be considered false.

However, the statement “if x=y, then x^2=y^2” would be true.

Why? For this question, I will assign x^2=81 for some clean numbers.

x^2=81

x^2=y^2

y^2=81.

Ok fair enough, right? Let’s take the square roots of both x^2 and y^2

x=+/-3

y=+/-3

In this case, x and y could both be 3, they could both be -3, or one is 3 and the other is -3. In the case that x and y are both 3 or -3, then the x=y part is true. However, if x = -3 and y = 3 (or vice versa), x is not equal to y.

In that statement, it is not guaranteed that if x^2=y^2 that x will always equal y. So if we were to ask “is the statement ‘if x^2=y^2, then x=y’ true or false?” we would answer false because if we said true, we would have to say yes every case is true. A “not necessarily” or a “not always” will automatically say false.