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Math Help - [SOLVED] set theory

  1. #1
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    [SOLVED] set theory

    How can we prove the image of the intersection of two sets does not necessarily equal the intersection of the images of the sets?
    And what can be the counter example?
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  2. #2
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    Quote Originally Posted by ninano1205 View Post
    How can we prove the image of the intersection of two sets does not necessarily equal the intersection of the images of the sets? And what can be the counter example?
    \begin{gathered}<br />
  f = \left\{ {\left( {1,a} \right),\left( {2,b} \right),\left( {3,a} \right),\left( {4,b} \right)} \right\} \hfill \\<br />
  A = \left\{ {1,2} \right\}\,\& \,B = \left\{ {3,4} \right\} \hfill \\<br />
  A \cap B = \emptyset \,\& \,f(A) \cap f(B) = ? \hfill \\ <br />
\end{gathered}
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