Discrete maths functions help

[JulianneK]

Hi all I was wondering if you could help me with this problem:

http://img713.imageshack.us/img713/4306/giflatexl.gif


Could someone explain this relationship in plain english for me please?

http://img9.imageshack.us/img9/338/codecogseqno.gif

This is what I was thinking, but I think it is wrong:

frogs(f) is a set of frogs where f is an element within the set F. Therefore frogs(toadie) is a set where toadie is an element of F. Therefore frogs(frogs(toadie)) means the set {toadie} is an element of F?

[LCKurtz]

You lost me with the first sentence. Seems to me if F is a set of frogs and f ε F, then f is a frog. So "the set of frogs of f" doesn't make sense to me.

Not being set theory expert, I may be missing something.