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Math Help - a "sets" question.

  1. #1
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    a "sets" question.

    Hello to everyone!
    Could someone say me the answer of the following set question?

    A ∩ B ⊆ A ∪ B = Prove!

    It needs a proving like the example below:

    A ∩ B = {x|xA and xB}

    Thanks,
    Best wishes.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kalle View Post
    Hello to everyone!
    Could someone say me the answer of the following set question?

    A ∩ B ⊆ A ∪ B = Prove!

    It needs a proving like the example below:

    A ∩ B = {x|x€A and x€B}

    Thanks,
    Best wishes.
    Lets consider the case where both sets are non-empty. the result holds trivially in the cases where both are empty or A \cap B is empty. (why?)

    to prove A \cap B \subseteq A \cup B we must show that if x \in A \cap B, then x \in A \cup B.

    Assume x \in A \cap B. Then x \in A and x \in B. Clearly it holds that x <br />
\in A or x \in B, so that x \in A \cup B. Thus, A \cap B \subseteq A \cup B
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