# Sets and axioms

1. Jan 12, 2010

### mathshelp

Let a and b be sets. Show that the following constructions are sets stating clearly which axioms you need

(a) a\b.

(b) A function f:a→ b.

(c) The image of f.

(d) Given that a and b have ranks α and β respectively, what are the maximum possible ranks of a\b, f:a→ b and the image of f?

I'm not sure of an answer for b and d at the moment.

For (a) i'm thinking ab= {x∈a: x is not in b} and therefore is a set by the subset axiom

and for (c) i'm thinking the image is {x∈b: there exists a y∈a, f(y)=x} which is a set by the subset axiom

What do you think?