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Math Help - Sets

  1. #1
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    Sets

    Consider the sets of values.

    A = {x: - infinity < x < 3}

    B = {x:3<x< infinity}

    C = {x:x=-3,3}

    Find = ( A intersect b ) union C.


    Would this be somthing like A = numbers between -3 and negative infinity

    b = numbers between 3 and positive infinity

    and c = numbers between -3 and 3?


    So a intersect b is any number between -3 and 3 and c union ( a intersect b ) is again between -3 and 3?
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  2. #2
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    Quote Originally Posted by el123 View Post
    Consider the sets of values.

    A = {x: - infinity < x < 3}

    B = {x:3<x< infinity}

    C = {x:x=-3,3}

    Find = ( A intersect b ) union C.


    Would this be somthing like A = numbers between -3 and negative infinity

    b = numbers between 3 and positive infinity

    and c = numbers between -3 and 3?


    So a intersect b is any number between -3 and 3 and c union ( a intersect b ) is again between -3 and 3?
    A \cap B = \emptyset ... they have no elements in common

    \emptyset \cup C = C

    as you have it written, C is a set with only two elements, 3 and -3.
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  3. #3
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    Thanks skeeter!
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  4. #4
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    Re: Sets

    Quote Originally Posted by el123 View Post
    Consider the sets of values.

    A = {x: - infinity < x < 3}

    B = {x:3<x< infinity}

    C = {x:x=-3,3}

    Find = ( A intersect b ) union C.


    Would this be somthing like A = numbers between -3 and negative infinity

    b = numbers between 3 and positive infinity

    and c = numbers between -3 and 3?


    So a intersect b is any number between -3 and 3 and c union ( a intersect b ) is again between -3 and 3?

    Sorry this is supposed to be
    a = {negative infinity < x < 3}

    b = {-3 < x < infinity.}

    c ={ x = -3 , 3}




    So as i see it , a intersect b = {-3<x<3}

    a intersect b includes all numbers between -3 and 3 but not -3 and 3 themselves.

    And since c includes only the values -3 and 3 , the union on (a intersect b) union c = nothing.???


    Is this correct?
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  5. #5
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    Quote Originally Posted by el123 View Post
    Sorry this is supposed to be
    a = {negative infinity < x < 3}

    b = {-3 < x < infinity.}

    c ={ x = -3 , 3}




    So as i see it , a intersect b = {-3<x<3}

    a intersect b includes all numbers between -3 and 3 but not -3 and 3 themselves.

    And since c includes only the values -3 and 3 , the union on (a intersect b) union c = nothing.???


    Is this correct?
    Considering your revisions, then, no, you are not correct. It is true that

    A\cap B = \{x: -3 < x < 3\},

    but now, since C=\{-3, 3\}

    we have

    (A\cap B)\cup C = \{x: -3\leq x \leq 3\}.
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  6. #6
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    ok i get it.

    So im right with the other values but since c contains -3, 3 and it is now a union of the values in a and b then all the values together are the values in (a intersect b) union c.


    Did i just make sense?
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  7. #7
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    Quote Originally Posted by el123 View Post
    ok i get it.

    So im right with the other values but since c contains -3, 3 and it is now a union of the values in a and b then all the values together are the values in (a intersect b) union c.


    Did i just make sense?
    I think so...

    Here's a tip: Think of intersection as "and" and union as "or." So for A\cap B we want all values that are in both A and in B. (A\cap B)\cup C is then all values that are in the first set or in C.
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