maybe I should do a counterexample along with it

let A = {1,2,3,4,5} and B = {1,3,5,6,7}

and have the function y = x^2

then

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- July 19th 2014, 08:51 PM #1

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## F(a-b)=f(a)-f(b)

Let X and Y be sets, and let A and B be any subsets of X.Determine if for all functions from X to Y, F(A-B) = F(A) - F(B) Justify your answer

intuition tells me no because the F(A-B) will have a different x values going to a different y values in Y than F(A) - F(B)

also,

the left side will have x values from X such that they are in

whereas the right side would have x values from X such that they are in

and clearly

- July 20th 2014, 10:57 AM #2

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- August 6th 2014, 07:47 AM #3

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## Re: F(a-b)=f(a)-f(b)

To get "{" and "}" in latex, you need to use "\{" and "\}"

Yes, that is correct.

**not**in Y". It does NOT mean "subtract members of Y from members of X"!

.

So again. This is**not**a "counter-example".