I need help in verifying the following please:
Let f:X→Y be a function, and let A,B⊆X, and let C,D⊆Y. Then
- f(A∩B)⊆f(A)∩f(B)
- f−1(C∩D)=f−1(C)∩f−1(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:X→Y be a function. Then the image of A under f is
f(A):={f(a)∈Y)(a∈A)}
and the preimage of C under f is
f−1(C):={(x∈X)(f(x)∈C)}.
So are the above definitions `missing' something? Thanks again.
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