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Thread: Trying to find sets obeying these subset relations (please help)

  1. #1
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    Exclamation Trying to find sets obeying these subset relations (please help)

    The elements of X are sets.

    Consider the subset relation R ("⊆") on X. (A, B) ∈ R iff A is a subset (⊆) of B.

    1. Give an example with |X| = 4 where relation "⊆" is a total order.


    This relation R is a Partial Order (POSET).

    My attempt...

    X = { {}, {1}, {1, 2}, {1, 2, 3} }. I'm not sure if this is correct.

    2. Give an example with |X| = 4 where the subset relation R does not contain any pair (A, B) with A ≠ B.

    I'm currently lost on this.

    3. Give an example with |X| = 6 where the subset relation does not contain any pair (A, B) with A ≠ B and all elements of X are subsets of the set {1, 2, 3, 4}.

    Lost on this, too.

    Cheers for assistance.
    Last edited by Induction; Sep 7th 2017 at 11:38 PM.
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  2. #2
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    Re: Trying to find sets obeying these subset relations (please help)

    Quote Originally Posted by Induction View Post
    The elements of X are sets.

    Consider the subset relation R ("⊆") on X. (A, B) ∈ R iff A is a subset (⊆) of B.

    1. Give an example with |X| = 4 where relation "⊆" is a total order.


    This relation R is a Partial Order (POSET).

    My attempt...

    X = { {}, {1}, {1, 2}, {1, 2, 3} }. I'm not sure if this is correct.

    Yes, that is correct.

    2. Give an example with |X| = 4 where the subset relation R does not contain any pair (A, B) with A ≠ B.

    I'm currently lost on this.
    It pretty much has to be "singleton" sets such as {{1}, {2}, {3}, {4}}.

    3. Give an example with |X| = 6 where the subset relation does not contain any pair (A, B) with A ≠ B and all elements of X are subsets of the set {1, 2, 3, 4}.

    Lost on this, too.

    Try {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}. No set is a subset of any other.


    Cheers for assistance.
    Last edited by HallsofIvy; Sep 8th 2017 at 04:23 AM.
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