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Math Help - Sets and functions

  1. #1
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    Sets and functions

    Any ideas about these?

    Prove that if f is a function, f^{-1}[A \cap B] = f^{-1}[A] \cap f^{-1} [b] .

    Also, prove that if f is a function, f^{-1}[A - B] = f^{-1}[A] - f^{-1} [b] .

    All of the B's should be capitalized, I'm not sure why it isn't coming out that way.
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  2. #2
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    x\in f^{-1}[A \cap B]
    f(x) \in A \cap B
    f(x) \in A and  f(x) \in B
    x\in f^{-1}[A] and x\in f^{-1}\left[B\right]
    x \in f^{-1}[A] \cap f^{-1}\left[B\right]

    check that each pair of consecutive lines is a pair of equivalent statements.


    x\in f^{-1}[A - B]
    f(x) \in A - B
    f(x) \in A and  f(x) \not \in B
    x\in f^{-1}[A] and x\not \in f^{-1}\left[ B \right]
    x \in f^{-1}[A] -f^{-1}\left[B\right]

    again check each pair of consecutive lines is a pair of equivalent statemetns.


    I am having the same problem with [b] as you, i tried \left[ B \right] and it worked.






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