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Math Help - Relation Problem !

  1. #1
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    Relation Problem !

    Let R and S be the relations on z by defined by

    a R b \iff a \equiv b\mod 9

    a S b \iff a \equiv b \mod 6

    Find (RUS)^{\infty} and \frac{A}{(RUS)^{\infty}}
    Attached Thumbnails Attached Thumbnails Relation Problem !-problem_1.gif   Relation Problem !-problem_2.gif  
    Last edited by mr fantastic; May 22nd 2009 at 03:41 AM. Reason: Tried to make the post intelligible
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by seamoh View Post
    > Suppose R and S be the relations on z by defined :a R b ⇔ a≡b(mod 9) aSb ⇔a[YOUTUBE]≡[/YOUTUBE]b mod 6) find (RUS)^(infinity )and A/(((RUS))^(infinity));

    >

    Do you mean find (R \cup S)^\infty as in everything in all the sets in (R \cup S)? There are a total of 19 such sets.

    If a, b \in R \cup S then a=9r+b=6s+b \Rightarrow 3r=2s. Thus, 2|r and 3|s (although the s follows from the formula every time you plug in the r). So, the elements related to i \in \mathbb{Z} under R and S are the elements, \{18r+1 : r \in \mathbb{Z} \}.

    What do you mean by the set A?
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