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Thread: sorts of sets

  1. #1
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    sorts of sets

    There is 3 relations between sets: superset, subset and equal.
    Are there more relations between sets?
    Are 3 relations include all the relations between sets that exist?
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  2. #2
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    Re: sorts of sets

    Quote Originally Posted by policer View Post
    There is 3 relations between sets: superset, subset and equal.
    Are there more relations between sets?
    Are 3 relations include all the relations between sets that exist?
    The answer depends upon what one means by relation.
    I thought at once about: two sets are disjoint provided that the have no elements in common.
    So what exactly do you mean?
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  3. #3
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    Re: sorts of sets

    Are subset, superset are relations (or there is another term to it)?
    Are the kinds (or sort, in the my bad English) of set influence on the defוnוtion of relations between sets?
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    Re: sorts of sets

    Quote Originally Posted by policer View Post
    Are subset, superset are relations (or there is another term to it)?
    Are the kinds (or sort, in the my bad English) of set influence on the defוnוtion of relations between sets?
    I sorry but I really do not know what that means.

    In addition to disjoint (as I posted above) here are others: complement, difference, symmetric difference,... to name a few.
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  5. #5
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    Re: sorts of sets

    Thanks.
    What is the definiton of:
    (1) difference,
    and (2) symmetric difference...
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    Re: sorts of sets

    Quote Originally Posted by policer View Post
    Thanks.
    What is the definiton of:
    (1) difference,
    and (2) symmetric difference...
    Set Difference -- from Wolfram MathWorld

    Symmetric Difference -- from Wolfram MathWorld
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  7. #7
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    Re: sorts of sets

    Quote Originally Posted by policer View Post
    What is the definiton of: (1) difference, and (2) symmetric difference...
    Assuming that you understand complement: Suppose that each of $A~\&~B$ is a set
    1) The difference of $A~\&~B$ is $A\setminus B=A\cap B^c$ some authors use $A-B$

    2) The symmetric difference is $A\Delta B=(A\cap B^{~c})\cup(B\cap A^c)=(A\setminus B)\cup(B\setminus A)$ some authors use $A\circleddash B$ or $A\oplus B$.
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