Defining a Function from a Set: A Practical Guide

[jsmith0476]

Let A = {{1,2},{1,3},{2},{2,5},{3,4,5}}. Define f : A-->N by f(a)=the sum of the elements of a (for all a that are a member of A).

I am just not sure how to define a function from a set. I have been really sick and haven't been able to make it to class :( Can someone point me in the right direction?

 

[jsmith0476]

So I have been reading some other posts and I think I understand it a bit more. Tell me if this would be right:

f( {2} ) = 2,
f( {1,2} ) = 1 + 2 = 3,
f( {1,3} ) = 1 + 3 = 4,
f( {2,5} ) = 2 + 5 = 7,
f( {3,4,5} ) = 3 + 4 + 5 = 12.

And so if I were to find the range of f it would be f = {2, 3, 4, 7, 12}??

 

[HallsofIvy]

Yes, that is exactly what "the sum of the elements of a" means! And since, as usual, "range of f" means "set of all values of f(a)", the range is {2, 3, 4, 7, 12} as you say.