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Where am I wrong?

  1. Jun 29, 2013 #1
    I know that f(A∩B) is not equal to f(A) ∩ f(B) but i don't know that where am i wrong in the following proof....:( can someone please give me an intuitive example? ImageUploadedByPhysics Forums1372525850.531238.jpg
     
  2. jcsd
  3. Jun 29, 2013 #2

    HallsofIvy

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    In order to prove "[itex]X= Y[/itex]" you must prove both "[itex]X\subseteq Y[/itex]" and [itex]Y\subseteq X[/itex].

    You want to prove that [itex]f(A\cap B)[/itex] is not equal to [itex]f(A)\cap f(B)[/itex] and your give proof shows only that [itex]f(A\cap B)\subseteq f(A)\cap f(B)[/itex].

    So look for a counter example in which [itex]f(A)\cap f(B)[/itex] is NOT a subset of [itex]f(A\cap B)[/itex].

    That is, find a function f and values p and q, p in A, q in B such that f(p)= f(q).
     
  4. Jun 29, 2013 #3
    Thank you sir.
    I understand your point & I can guess the best example is one to many which is not true, & i have tried to show it in proof.
    ImageUploadedByPhysics Forums1372546039.352093.jpg
     
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