# 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*}