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Thread: Question on Function Proof

  1. #1
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    Question on Function Proof

    Would someone please help me with the answer to this question please:
    (it is a prep question for the qualifier and taken from an old exam)

    Assume a function f: A->B and sets A1, A2 $\displaystyle \subseteq$ A, for which f(A1 $\displaystyle \cap$ A2) $\displaystyle \neq$ f(A1)$\displaystyle \cap$ f(A2).
    Demonstrate this inequality.
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  2. #2
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    Quote Originally Posted by itpro View Post
    Assume a function f: A->B and sets A1, A2 $\displaystyle \subseteq$ A, for which f(A1 $\displaystyle \cap$ A2) $\displaystyle \neq$ f(A1)$\displaystyle \cap$ f(A2).
    Demonstrate this inequality.
    $\displaystyle A=\{1,2\},~B=\{a,b\}~\&~f=\{(1,b),(2,b)\}.$

    $\displaystyle A_1=\{1\}~\&~A_2=\{2\}$ then $\displaystyle f(A_1\cap A_2)=?$.

    $\displaystyle f(A_1)\cap f(A_2)=?$
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