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Math Help - Set question

  1. #1
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    Set question

    If U = {3, 4, 5} and U union V = {1,2,3,4,5}

    The set V I am told must have the fewest number of members as possible. Am I right in thinking that the members of the set V must be:

    V = {1, 2}
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Natasha1 View Post
    If U = {3, 4, 5} and U union V = {1,2,3,4,5}

    The set V I am told must have the fewest number of members as possible. Am I right in thinking that the members of the set V must be:

    V = {1, 2}
    Yes, that's correct based on what you've been told.

    However, I believe we have more options: V = {1,2} , {1,2,3}, {1,2,4}, {1,2,5}, {1,2,3,4}, {1,2,3,5}, {1,2,4,5}, or {1,2,3,4,5}.
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  3. #3
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    Thanks. I am just a little perplex because if V = {1, 2} would that not mean that there would actually not be any union.

    You'd have U = {3, 4, 5} and V = {1, 2} but completely separate and not sharing any members...

    I am a little confused
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Natasha1 View Post
    Thanks. I am just a little perplex because if V = {1, 2} would that not mean that there would actually not be any union.

    You'd have U = {3, 4, 5} and V = {1, 2} but completely separate and not sharing any members...

    I am a little confused
    The union is defined to be: A\cup B=\{x : x\in A\text{ or }x\in B\text{ or in both}.\}. So it turns out that there doesn't need to be an overlap between two sets in order to take their union. If there is an overlap, you would count that element just once.

    However, if you ended up taking the intersection, it would be empty because there are no common elements.
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  5. #5
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    many thanks
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