Just a simple question #6

Number Theory Level 1

Which of these statements are true?

(A). " $1$ is a prime number"

(B). " $0$ is neither even nor odd"

(C). " $\sqrt{x^2}$ is always equal to $x$ "

(D). " $\dfrac{1}{4}$ is neither even nor odd"

All of these B D None of these A C

1 solution

Andronikus Lumembang
Feb 6, 2015

The definition of prime number is a number of which has only two factors. $1$ has only one factor, so it's not a prime number.
$0$ is an even number. Because it's an integer multiple of two $( 0 \times 2 = 0)$ .
$\sqrt{x^2} = |x|$
The concept of even and odd number is only applied to integers. $\dfrac{1}{4}$ isn't an integer, so it's neither even nor odd number

There are so many other proves about the statements. Let's just leave it for the discussion.

I should have read the question more carefully

Evan Huynh - 4 years, 9 months ago

Can anyone explain why parity does not apply to non-integers?

Tom Hass - 2 years, 1 month ago

I guess I didn't know how to determine whether or not a fraction is even or odd. They never taught me this back when I was in public school. I thought only integers could be even or odd but wasn't sure.

Christopher Nilsson - 1 year, 1 month ago

Ahhhh, the absolute value of x... Good one!

Meridith Burton - 9 months, 1 week ago

I used the same reasoning for all except statement (3). Keep in mind that $\sqrt{x^2} = |x|$ only if x is a real number. More generally, $\sqrt{x^2} \neq x$ except for specific $x$ , which is my solution.

Caleb Townsend - 6 years, 4 months ago

Nice solution, bro.

Resha Dwika Hefni Al-Fahsi - 4 years, 11 months ago

Just a simple question #6

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