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Math Help - logic sets help

  1. #1
    Junior Member
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    logic sets help

    can anyone do this question?
    Attached Thumbnails Attached Thumbnails logic sets help-1.jpg  
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  2. #2
    Senior Member
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    Hey

    Do you know what Z6 means? What exactly is your question?

    (1*1) mod 6 = 1
    (1*2) mod 6 = 2
    ....
    (1*5) mod 6 = 5

    (2*1) mod 6 = (1*2) mod 6 = 2
    (2*2) mod 6 = 4
    (2*3) mod 6 = 6 mod 6 = 0
    (2*4) mod 6 = 8 mod 6 = 2
    (2*5) mod 6 = 10 mod 6 = 4

    ....

    and so on.
    Does it help?

    Regards, Rapha
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  3. #3
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    Hello, srk619!

    Rapha is right . . .
    You're expected to know what \mathbb{Z}_6 means.
    If you don't, you shouldn't have been assigned this problem.


    Give the multiplication table for \mathbb{Z}_6

    and hence find all solutions to: . x^2 \,=\,3\:\text{ in }\mathbb{Z}_6 or explain why there are none.

    . . \begin{array}{c||c|c|c|c|c|c|}<br />
\times & 0&1&2&3&4&5 \\ \hline \hline<br />
0 & 0&0&0&0&0&0 \\ \hline<br />
1 & 0&1&2&3&4&5 \\ \hline<br />
2 & 0&2&4&0&2&4 \\ \hline<br />
3 & 0&3&0&3&0&3 \\ \hline<br />
4 & 0&4&2&0&4&2 \\ \hline<br />
5 & 0&5&4&3&2&1 \\ \hline\end{array}


    The values for x^2 are on the main diagonal,

    . . where we see that: . 3\cdot3 \:=\:3\text{ (mod 6)}


    Therefore: . x = 3

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  4. #4
    Junior Member
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    Nov 2008
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    the question is part of Integers, Congruence arithmetic

    its something like what is in the diagram
    Attached Thumbnails Attached Thumbnails logic sets help-1a.jpg  
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