I'm trying to learn discrete math and I'm lost as to why this truth value is true. Can anyone please explain why? The domain consists of all real numbers.
$∀x((-x)^2=x^2)$
The answer is True, but I can't see why that's so.
I'm reading this as for the set of all real numbers, $-x^2=x^2$, which if I just choose a random number, like say 1, I get -1=1. What's up with this? Am I way missing something?
Thanks.
Andre Nicolas gave me the correct answer. Thanks again!
$$(-x)^2 = (-x)\cdot(-x) = (-1)\cdot(-1)\cdot x^2=x^2$$ Hence for $x=1$
$$(-1)^2 = (-1)\cdot(-1) = (-1)\cdot(-1)=1^2=1$$