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Thread: number of relations between two sets

  1. #1
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    number of relations between two sets

    Sir / Madam,

    The total number of relations that can be defined from a set A to a set B
    is the number of possible subsets of A B. If n(A ) = p and n(B) = q, then
    n (A B) = pq and the total number of relations is 2pq (we say).

    However, doesn't 2pq. also count the null set of ordered pairs as a relation? whether to count a null set of ordered pairs as a relation?

    kindly enlighten me.

    with regards

    Aranga
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  2. #2
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    Re: number of relations between two sets

    Well, what, exactly, is your definition of "relation"? Does the empty set fit that definition?
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    Re: number of relations between two sets

    I am asking generally. Suppose if set A = {a,b,c} and set B = {1,2,3} What are all the possible relations between A and B.
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    Re: number of relations between two sets

    Quote Originally Posted by arangu1508 View Post
    I am asking generally. Suppose if set A = {a,b,c} and set B = {1,2,3} What are all the possible relations between A and B.
    Again, It depends on the definition of Binary relation you use.
    Look at this definition at Wolfram's MathWorld.
    There is says "ANY subset of $A\times B$. Thus that includes $\emptyset$.
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  5. #5
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    Re: number of relations between two sets

    You need to specify the binary relation you use. Because the result may depend on it.
    Last edited by Plato; Jan 24th 2018 at 10:33 AM. Reason: Removed SPAM
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    Re: number of relations between two sets

    Quote Originally Posted by SummerStudy View Post
    You need to specify the binary relation you use. Because the result may depend on it.
    That is a false statement. The question asks "How many relations are there between two sets(finite): $A\to B$
    Your [b]definition of "any relation" can make a difference in the number, but not a particular relation.
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