Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By romsek

Thread: Please Solve this question of Discrete mathematics

  1. #1
    Newbie
    Joined
    May 2014
    From
    Okara
    Posts
    9

    Please Solve this question of Discrete mathematics

    Let D and S be relations on A = {0, 1, 2, 3}.
    D = {(a, b) | b = (3a+1) mod 4}
    S = {(a, b) | b < a+1}
    D = {(0, 4), (1, 16), (2, 28), (3, 40)}
    S = {(1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3)}

    SD =???????????

    Then find values of SD by writing all the intermediate steps
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,161
    Thanks
    2615

    Re: Please Solve this question of Discrete mathematics

    have you made any effort at it yet?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,466
    Thanks
    1377

    Re: Please Solve this question of Discrete mathematics

    Either your first two definitions for D and S are wrong or the second two are. My guess is the second two are. Note: If $\displaystyle D = \{(0,4),(1,16),(2,28),(3,40)\}$, then $\displaystyle D \not \subset A\times A$, so it is not a relation on $\displaystyle A$

    Based on the first definition, $\displaystyle D = \{(0,1), (1,0), (2,3), (3,2)\}$

    Similarly, the $\displaystyle S$ you gave does not match the definition you gave, nor is it even a relation on $\displaystyle A$. Using the first definition,

    $\displaystyle S = \{(0,0),(1,0),(1,1),(2,0),(2,1),(2,2),(3,0),(3,1), (3,2),(3,3)\}$

    Next, use the definition for composition of binary relations.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2014
    From
    Okara
    Posts
    9

    Re: Please Solve this question of Discrete mathematics

    Dear sir Bundle of thanks for guiding me. After posting my question I realized that I solved D and S were really wrong. Sir my question is still incomplete because I want to find SD =???????????
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2014
    From
    Okara
    Posts
    9

    Re: Please Solve this question of Discrete mathematics

    I find SD={(0,0),(0,1),(1,0),(2,0),(2,1),(2,2),(2,3),(3, 0),(3,1),(3,2)}. is am I correct????? or Not. If not then please find SD=????????????
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,800
    Thanks
    2829
    Awards
    1

    Re: Please Solve this question of Discrete mathematics

    Quote Originally Posted by ahsanalisony View Post
    Let D and S be relations on A = {0, 1, 2, 3}.
    D = {(a, b) | b = (3a+1) mod 4}
    S = {(a, b) | b < a+1}
    $S\circ D =?$
    First the set $A$ has only four elements. Therefore, any relation can have at most sixteen pairs.

    To do this question you must know what relations look like:
    $D=\{(0,1)~,(1,0)~,(2,3)~,(3,2)\}$ and
    $S=\{(0,0)~,(1,0)~,(1,1)~,(2,0)~,(2,1)~,(2,2)~,(3, 0)~,(3,1)~,(3,2)~,(3,3)\}$

    Now, try again!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,466
    Thanks
    1377

    Re: Please Solve this question of Discrete mathematics

    To calculate $\displaystyle S\circ D$, take all of the pairs of $\displaystyle S$ and pairs of $\displaystyle D$ where the second coordinate from the pair in $\displaystyle S$ is the same as the first coordinate of the pair in $\displaystyle D$ and group them together:

    Pairs in $\displaystyle S$ where the second coordinate is zero:
    $\displaystyle (0,0), (1,0), (2,0), (3,0)$

    Pairs in $\displaystyle D$ where the first coordinate is zero:
    $\displaystyle (0,1)$

    Each pair from $\displaystyle S$ and that single pair from $\displaystyle D$ form pairs in $\displaystyle S\circ D$:
    $\displaystyle (0,1), (1,1), (2,1), (3,1)$
    (That is the first coordinate from the pair in $\displaystyle S$ and the second coordinate from the pair in $\displaystyle D$)

    Now, do the same for pairs in $\displaystyle S$ where the second coordinate is one and pairs in $\displaystyle D$ where the first coordinate is one. Then move on to when they are both two, and finally when they are both three. That will give you all elements of $\displaystyle S\circ D$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 16th 2014, 01:50 PM
  2. Discrete Mathematics GCD Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Feb 5th 2010, 11:48 AM
  3. Discrete mathematics question
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Feb 4th 2010, 01:55 PM
  4. Mathematics: Discrete-Mathematics (Algorithems)
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Nov 2nd 2008, 06:27 AM
  5. Generic Question Discrete mathematics
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Sep 11th 2007, 08:10 PM

Search Tags


/mathhelpforum @mathhelpforum