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Math Help - Binary Relation and Range

  1. #1
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    Question Binary Relation and Range

    I have a question with solution and want to understand how we get the range given in the solution ?

    Question
    If L={a,b,c,d} and M={3,4} then find two binary relations of L*M

    Solution
    L*M={(a,3),(a,4),(b,3),(b,4),(c,3),(c,4),(d,3),(d, 4)}
    Two binary relations of L*M are as follows:

    R1={(a,3),(b,4),(c,3)}

    R2={(a,4),(b,3),(c,4)}
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  2. #2
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    Re: Binary Relation and Range

    Quote Originally Posted by haftakhan View Post
    Question
    If L={a,b,c,d} and M={3,4} then find two binary relations of L*M

    Solution L*M={(a,3),(a,4),(b,3),(b,4),(c,3),(c,4),(d,3),(d, 4)}
    Two binary relations of L*M are as follows:
    R1={(a,3),(b,4),(c,3)}
    R2={(a,4),(b,3),(c,4)}
    The range is simply the set of second terms: \text{Rng}(R_1)=\{3,4\}~.
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  3. #3
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    Re: Binary Relation and Range

    Quote Originally Posted by Plato View Post
    The range is simply the set of second terms: \text{Rng}(R_1)=\{3,4\}~.
    Actually my question should have been that how we get
    R1={(a,3),(b,4),(c,3)}
    R2={(a,4),(b,3),(c,4)} ?
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  4. #4
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    Re: Binary Relation and Range

    Quote Originally Posted by haftakhan View Post
    Actually my question should have been that how we get
    R1={(a,3),(b,4),(c,3)}
    R2={(a,4),(b,3),(c,4)} ?
    There are 12 ordered pairs in L\times M.
    A relation is any subset of those pairs. So there are 2^{12} possible relations.

    Those are just two of them. There is no rule.
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  5. #5
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    Re: Binary Relation and Range

    Quote Originally Posted by Plato View Post
    There are 12 ordered pairs in L\times M.
    A relation is any subset of those pairs. So there are 2^{12} possible relations.

    Those are just two of them. There is no rule.
    It means that i can write any ordered pair in R1={(a,3),(b,4),(c,3)} instead of the three given?
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  6. #6
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    Re: Binary Relation and Range

    Yes, a "binary relationship" between set A and set B is any subset of A\times B. That is, any set of ordered pairs where the first member of each pair is from A and the second member if from B.
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