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Math Help - Proving Intersections and Unions

  1. #1
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    Proving Intersections and Unions

    (A intersect B) is contained in A is contained in (A union B)

    I know I have to show containment both ways, meaning
    (A intersect B) is contained in A
    A is contained in (A union B)

    Can you help me get started?
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  2. #2
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    Re: Proving Intersections and Unions

    To prove that X is contained in Y, show that every element of X is an element of Y. Use the definitions of union and intersection.
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  3. #3
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    Re: Proving Intersections and Unions

    Quote Originally Posted by lovesmath View Post
    (A intersect B) is contained in A is contained in (A union B)

    I know I have to show containment both ways, meaning
    (A intersect B) is contained in A
    A is contained in (A union B)
    Can you help me get started?
    If x\in A\cap B then x\in A~\&~x\in B therefore x\in A. That means A\cap B\subseteq A.
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  4. #4
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    Re: Proving Intersections and Unions

    The way you prove " X\subseteq Y" is to start "if x is in X" then use the definitions of X and Y to show "then x is in Y". As Plato said, " A\cap B" is defined as the set of all x such that x is in A and x is in B. If x\in A\cap B then x\in A. Now, you need to show "if x\in A then x\in A\cup B". So, what is the definition of " A \cup B"?
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