# Set notation for conditional

I have a function $$g()$$ that maps a tuple to a set.

$$g(f_1,f_2,...,f_n) = a.$$

• $$a$$ is a subset of the natural numbers.

• The tuple has binoard indicators.

Now, say $$n=3,$$ the function works as follows:

$$g(0,1,1) = \{2,3\}.$$

I want to write in set notation how this function works, all I can get to is this:

$$g(f_1,f_2,...,f_n) = a$$ where $$a = \{1 \text{ if } f_1 = 1, 2 \text{ if } f_2=1,\dots ,n \text{ if } f_n=1\}.$$

So this is how the function works, but obviously there is a better way to write this mathematically, any help? Thx

What you're suggesting is that $$k \in g(f_1, \dots, f_n)$$ if and only if $$f_k = 1$$. So you could use set-builder notation to write $$g(f_1, f_2, \dots, f_n) = \{ k \mid f_k = 1 \}$$