Logic problem: Truth value of statement the product of $x^2$ and $x^3$ is $x^6$

Question

I want to understand why these statements below are false. I assumed that the statements are true because they are real numbers

Without any quantifier, the first one is not even a statement, since it depends on $x$ (it doesn't matter that it's true for each real $x$), hence is neither true nor false. The second one is just false because it fails for $x=0$. — Wojowu, Jan 15 '19 at 10:13
@JoseArnaldoBebitaDris ...can we pretend I never said that? :P — Wojowu, Jan 15 '19 at 10:19
@bof probably not, as OP is trying to figure out why the given statements are false. — StackTD, Jan 15 '19 at 10:20
FWIW, the first statement is true if $x = 0$ or $x=1$, and false otherwise. — Jose Arnaldo Bebita Dris, Jan 15 '19 at 10:22

score 3 · Accepted Answer · answered Jan 15 '19 at 10:14

3

The product of $x^2$ and $x^3$ is $x^6$

Do you know a rule for $\boxed{x^m x^n = \ldots}$ ?

Don't confuse it with the rule for $\boxed{\left(x^m\right)^n = \ldots}$ !

If not, look them up.

The $x^2>0$ for any real number $x$

But also $0$ is a real number, so...

answered Jan 15 '19 at 10:14

StackTD

FWIW, the first statement is true if $x = 0$ or $x=1$, and false otherwise. – Jose Arnaldo Bebita Dris Jan 15 '19 at 10:21
It's hard to tell if OP copied the problem literally or not; I'm trying to answer in the spirit of what I assume to be the underlying idea of the question. Of course the question would benefit from a more precise phrasing. – StackTD Jan 15 '19 at 10:27

1 Answers1