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Math Help - equivalent relations help

  1. #1
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    equivalent relations help

    Hey guys, having trouble with the following question.
    Let A = {1,2,3,4},

    a) how many relations are there on A?

    My answer: \mathcal{P}(A \cdot A) = 2^{4 \cdot 4} = 2^{16}

    b) How many equivalent relations are there on A?

    My answer: Im not sure about this one. Any help?
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    Let A = {1,2,3,4},
    a) how many relations are there on A?

    My answer: \mathcal{P}(A \cdot A) = 2^{4 \cdot 4} = 2^{16} CORRECT

    b) How many equivalent relations are there on A?
    Before I answer please answer this.
    Does you textbook/instructor really use the notation A\cdot A for the cross product of A with itself?
    The almost standard notation is A\times A.

    For the help. There is a one-to-one correspondence between the partitions of the set and the equivalence relations on the set.
    You want to find the fourth Bell number.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Before I answer please answer this.
    Does you textbook/instructor really use the notation A\cdot A for the cross product of A with itself?
    The almost standard notation is A\times A.

    For the help. There is a one-to-one correspondence between the partitions of the set and the equivalence relations on the set.
    You want to find the fourth Bell number.
    No they use A\times A but I didnt know the latex symbol for x. Now I do

    Not sure what you mean by fourth Bell number.....
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  4. #4
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    Quote Originally Posted by jvignacio View Post
    No they use A\times A but I didnt know the latex symbol for x. Now I do

    Not sure what you mean by fourth Bell number.....
    Do a web search for Bell Numbers.
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