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Math Help - Set question #1

  1. #1
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    Set question #1

    Why ( A \subseteq B ) \equiv [ A \cap B = A ] \equiv [ A \cup B = B ] ?
    Why A \cap ( B - C ) = ( A \cap B) - ( A \cap C) ?
    Why A - B = A \oplus  ( A \cap B )
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  2. #2
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    Quote Originally Posted by Researcher View Post
    Why ( A \subseteq B ) \equiv [ A \cap B = A ] \equiv [ A \cup B = B ] ?
    Why A \cap ( B - C ) = ( A \cap B) - ( A \cap C) ?
    Why A - B = A \oplus  ( A \cap B )
    These are so basic, what is your problem? Do you know basic definitions?
    What does A \subseteq B mean to you?
    What does A \cap B mean to you?
    What does A \cup B mean to you?
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  3. #3
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    Quote Originally Posted by Plato View Post
    These are so basic, what is your problem? Do you know basic definitions?
    What does A \subseteq B mean to you?
    What does A \cap B mean to you?
    What does A \cup B mean to you?
    I know the meanings of them.
    I know they seem true intuitively, but i want their proofs!!
    I can prove the 3rd. But in proving the 2nd i get a contradiction!
    Now can you help me?
    If it's necessary, i can show the contradiction.
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  4. #4
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    Quote Originally Posted by Researcher View Post
    But in proving the 2nd i get a contradiction!
    x \in A \cap B \Leftrightarrow \left[ {\left( {x \in A} \right) \wedge \left( {x \in B} \right)} \right]
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  5. #5
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    What about the others?
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  6. #6
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    Quote Originally Posted by Researcher View Post
    What about the others?
    What about them?
    All I posted above is the basic definition.
    Again I ask, do you know the definitions?
    These posts lead me to think that you do not.
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  7. #7
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    I know what you posted is. And i told you i know the basic meanings and don't need to know them by you.
    I meant give up defining the meaning of intersection for me, pay attention to the questions.

    However I solved the first afew minutes ago!
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