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Thread: Proving a set theory

  1. #1
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    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.
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  2. #2
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    Re: Proving a set theory

    Quote Originally Posted by inayat View Post
    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?
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  3. #3
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    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.
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