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

Then,

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??