Monday, 1 May 2017

functions - Verifying a proposition on image and preimage: f(AcapB)subseteqf(A)capf(B) and f1(CcapD)=f1(C)capf1(D)

I need help in verifying the following please:




Let f:XY be a function, and let A,BX, and let C,DY. Then




  • f(AB)f(A)f(B)

  • f1(CD)=f1(C)f1(D)





I am not quite certain how to get started, and would appreciate any help. Thanks.






Edit:



Please excuse my ignorance, but I think that part of the trouble I am having is notational, since I only have this proposition from one book and the definitions of image and preimage from another. Here is what I have for the definitions:




Let f:XY be a function. Then the image of A under f is
f(A):={f(a)Y)(aA)}
and the preimage of C under f is
f1(C):={(xX)(f(x)C)}.



So are the above definitions `missing' something? Thanks again.

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