properties of functions problem
Let S be a set and A, B and C be finite subsets of S. Consider the functions:
I. sum(numbers) = sum of the numbers
II. count(A) = number of elements in A
III. int(A, B) = intersection of A and B
IV. uni(A, B) = union of A and B
V. dif(A, B) = difference of A and B
a) Write the type of each of the previous functions
b) Express each the counting rules for
i. A – (B U C)
ii. A U B U C
iii. A – B
as compositions of the previous functions
c) For each of these compositions: are they injective? Are they onto?
I have no clue how to approach this problems any suggestions??