Functions on sets

Oct 2015
Let X and Y be sets, let A and B be any subsets of X, and let C and D be any subsets of Y. Dertermine which of the properties are true for all functions F from X to Y and which are false for at least one function F from X to Y. Justify your answers.

For all subsets A and B of X, F(A-B) = F(A) - F(B)

Country Boy

Math Team
Jan 2015
Let X be {a, b, c, d, ..., x, y, z}, Y= {0, 1, 2, 3, 4, 5, 6, 7, 8 , 9}. Take A= {a, b, c, d, e}, B= {a, b, c} and F mapping every member of X to 0. What is A- B? What is F(A- B)? What are F(A) and F(B)? What is F(A)- F(B)?