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Math Help - If |X|=5, how many non-ordered pairs {A,B} consisting of disjoint subsets exist?

  1. #1
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    If |X|=5, how many non-ordered pairs {A,B} consisting of disjoint subsets exist?

    Hi, I have the following exercise, but I don't know how to solve it so any help you can give me would be great... Thanks!

    It says

    Suppose that |X|=5. Find how many non-ordered pairs {A,B} consisting of non-empty disjoint subsets A and B of the set X exist.
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  2. #2
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    How many pairs of singletons could you draw from the power set? <single, single>

    How many pairs of any one pair and the triple which is disjoint to it could you draw? <pair, triple>

    How many distinct pairs of one pair and one of the 3 pairs disjoint to it could you draw? <pair, pair>

    How many pairs of any one pair and one of the 3 singletons disjoint to it could you draw? <pair, single>

    How many pairs of any triple and one of the 2 singletons disjoint to it? <triple, single>

    How many pairs of any quadruple and the singleton disjoint to it? <quadruple, single>
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  3. #3
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    @tom@ballooncalculus
    Where have you considered the \emptyset in any of your counting?
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  4. #4
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    Quote Originally Posted by Plato View Post
    @tom@ballooncalculus
    Where have you considered the \emptyset in any of your counting?
    The question says not to.

    Don't you need to do a little more though, considering different possibilities for, e.g., the particular 4-subset?
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  5. #5
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    Well, for any of the 5 particular quadruples (each giving a pairing of that quadruple with its disjoint single), no. What different possibilities do you see?
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  6. #6
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    Like you said, 5 possibilities.

    Maybe it's just the way you interpret what your wrote... I'm reading it as counting for one fixed quadruple instead of all possible ones.
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