Results 1 to 2 of 2

Thread: Relation Problem !

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    5

    Relation Problem !

    Let $\displaystyle R$ and $\displaystyle S$ be the relations on z by defined by

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

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

    Find $\displaystyle (RUS)^{\infty}$ and $\displaystyle \frac{A}{(RUS)^{\infty}}$
    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    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 $\displaystyle (R \cup S)^\infty$ as in everything in all the sets in $\displaystyle (R \cup S)$? There are a total of $\displaystyle 19$ such sets.

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

    What do you mean by the set $\displaystyle A$?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. relation problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 17th 2011, 08:17 AM
  2. another relation problem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Aug 6th 2008, 02:30 PM
  3. Still need help with relation problem
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: Mar 20th 2008, 11:14 AM
  4. Relation Problem
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: Feb 21st 2008, 07:02 PM
  5. Relation Problem
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Feb 28th 2007, 06:25 AM

Search Tags


/mathhelpforum @mathhelpforum