# Thread: Proving a set theory

1. ## Proving a set theory

Please can someone help me with this:

http://prntscr.com/h9a42p

I need to prove,

i understand that there's a remainder 2 at left side

No remainder at right side

Not sure how to proceed after that.

2. ## Re: Proving a set theory

Originally Posted by inayat
Please can someone help me with this:

http://prntscr.com/h9a42p

I need to prove, $\{3k+2: k\in\mathbb{N}\}\cap\{12\ell: \ell\in\mathbb{N}\}=\emptyset$

i understand that there's a remainder 2 at left side
No remainder at right side
Suppose that for some $k~\&~\ell$ are such that:
\begin{align*}3k+2&=12\ell \\12\ell-3k&=2\\3(4\ell-k) &=2\end{align*}

What is the contradiction there? Or even is there a contradiction?

3. ## Re: Proving a set theory

Surely it is not so blasted hard to type "Show that the set of all number of the form 3k+ 2, where k is an integer, intersect the set of all numbers of the form 12l, where l is an integer is empty" that you had to go to the trouble of posting a screenshot and expecting us to open another site to read it!

You know, I hope, the 12= 4(3) is a multiple of 3 so that any multiple of 12 is also a multiple of 3. But "3k+ 2" is NOT a multiple of 3.