Hi i have the following question from an old exam paper im stuck on, its a three part question and goes as follows:

(b) Which of the following functions are surjective, injective or bijective? If it is bijective,

write down the inverse function. (Justify your answers.)

(i)

*f *: Z12 *→ *Z12 : *f*([*a*]12) = [*a*]12 *· *[5]12;

(ii) *f *: Z12 *→ *Z12 : *f*([*a*]12) = [*a*]12 *· *[3]12.

[ 10 marks ]

(c) Let *A *be the set of 3-digit decimal integers *{*000*, *001*, *002*, . . . , *999*}*. Use the Inclusion-

Exclusion Principle to find how many elements of *A *are not divisible by 2, nor by 3, nor by

5. (It may be useful to denote by *A*2 the set of 3-digit decimal integers that are divisible by

2.)

The first question i have tried to find examples of this in text books but with no luck, i realsie that a one-one function is injective and is described as a function for which different inputs give different outputs, i am fine in the case of f: N->N where f(x)=x^2 but the format in which the question is shown above i havent got a clue

For the inclusion and exclusion i am aware it will be something to do with the AuBuC equation mate letting a= not divisible by 2, b= not divisible by 2 etc then to find the relevant A and B etc to plug into the equation?

Any help would be most appreciated, thanks in advance.