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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.


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?


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It says that $(-x)^2=x^2$. Note the parentheses: $(-x)^2$ is the square of $-x$. So $(-1)^2=1$. – André Nicolas Jan 12 '13 at 5:01
wow, duh. my brain is friend from too much math today. i was trying to prove this to myself with a calculator and was using the x^2 button, but of course, was using it incorrectly. – user56763 Jan 12 '13 at 5:05
Please try to use more descriptive titles. – Rahul Jan 12 '13 at 6:06

Andre Nicolas gave me the correct answer. Thanks again!

$$(-x)^2 = (-x)\cdot(-x) = (-1)\cdot(-1)\cdot x^2=x^2$$ Hence for $x=1$

$$(-1)^2 = (-1)\cdot(-1) = (-1)\cdot(-1)=1^2=1$$

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