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Math Help - Relations and Functions - Inverse Relations Question

  1. #1
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    Relations and Functions - Inverse Relations Question

    Let S = {a,b,c,d,e} be a set of senators and P = {w,x,y,z} be a set of policies. Let RCS*P be the relation defined by sRp if s supports p.

    Q1: Define the inverse relation: R^(-1)

    my answer: R^(-1) = {(p,s) (element of) P*S; (s,p) (element of) R}


    Q2: What does pR^(-1)s mean?

    my answer: pR^(-1) s means sRp


    Q3: What is {s (element of) S; pR^(-1) s}

    Don't know the answer to this one.


    Are my first two answers correct, and how would I answer the third question? Thanks in advance.
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  2. #2
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    Re: Relations and Functions - Inverse Relations Question

    Quote Originally Posted by maclunian View Post
    Q1: Define the inverse relation: R^(-1)

    my answer: R^(-1) = {(p,s) (element of) P*S; (s,p) (element of) R}
    Correct.


    Quote Originally Posted by maclunian View Post
    Q2: What does pR^(-1)s mean?

    my answer: pR^(-1) s means sRp
    I think the question asked to describe the relation R^{-1} in words, similar to how sRp means "s supports p."

    Quote Originally Posted by maclunian View Post
    Q3: What is {s (element of) S; pR^(-1) s}

    Don't know the answer to this one.
    If you do Q2, then it is easy to describe the set \{s\in S: pR^{-1}s\} in words for each particular p.
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