# I Determining which statement is true (1 Viewer)

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#### ver_mathstats

We are given several statements and we must determine which one is true, n is a fixed positive integer, it asks which statement is true regardless of which positive integer n you choose?

The first one states that if n is divisible by 6, then n is divisible by 3.
I chose 12 for n and it was true.
I chose 18 for n and it was true as well.
Does this mean that the statement is true? Because I believe it is true.

Another one states if n is divisible by 3, then n is divisible by 6.
This one is still true because if you substitute 12 and 18 it still holds true.

Another one also states that if n2 is divisible by 6, then n is divisible by 6.
I chose 6 for n and it held true, ((6)2)/6 and 6/6 worked out meaning it must be true.

Is this the correct way to solve this question or am I doing it incorrectly?

Thank you.

#### stockzahn

Homework Helper
Gold Member
We are given several statements and we must determine which one is true, n is a fixed positive integer, it asks which statement is true regardless of which positive integer n you choose?

Is this the correct way to solve this question or am I doing it incorrectly?
Good morning,

first of all, if this is some kind of homework please use the homework forum with its template. Secondly, it doesn't suffice to prove a mathematical statement with two examples, so I think you should find a proof, which applies for the infinity of numbers (or one converse example for disprooving).

The first one states that if n is divisible by 6, then n is divisible by 3.
I chose 12 for n and it was true.
I chose 18 for n and it was true as well.
Does this mean that the statement is true? Because I believe it is true.
Assumption: $n\;mod\;6 = 0 \rightarrow n\;mod\;3 = 0$
$6 = 2\cdot 3$
$\frac{n}{6} = \frac{n}{2\cdot 3} = \frac{1}{2}\frac{n}{3} \rightarrow \frac{n}{3}\;mod\;2 = 0$
The modulo of a number only can be zero, if it is integral, therefore $\frac{n}{3}$ must be an integral and $n\;mod\;3 = 0$

Another one states if n is divisible by 3, then n is divisible by 6.
This one is still true because if you substitute 12 and 18 it still holds true.
What about the $n=9$?

Another one also states that if n2 is divisible by 6, then n is divisible by 6.
I chose 6 for n and it held true, ((6)2)/6 and 6/6 worked out meaning it must be true.
Try by yourself. Find a chain of assumptions and proofs or one disprooving example to verify or falsify the assumption.

#### ver_mathstats

Good morning,

first of all, if this is some kind of homework please use the homework forum with its template. Secondly, it doesn't suffice to prove a mathematical statement with two examples, so I think you should find a proof, which applies for the infinity of numbers (or one converse example for disprooving).

Assumption: $n\;mod\;6 = 0 \rightarrow n\;mod\;3 = 0$
$6 = 2\cdot 3$
$\frac{n}{6} = \frac{n}{2\cdot 3} = \frac{1}{2}\frac{n}{3} \rightarrow \frac{n}{3}\;mod\;2 = 0$
The modulo of a number only can be zero, if it is integral, therefore $\frac{n}{3}$ must be an integral and $n\;mod\;3 = 0$

What about the $n=9$?

Try by yourself. Find a chain of assumptions and proofs or one disprooving example to verify or falsify the assumption.
I was unaware of the homework template, I shall start using that now, my apologies. Thank you for the help. I am going to retry the question right now.

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