Question

Write out all functions f : {1, 2, 3} → {a, b} (using two-line notation). How many functions are there?

Answer 1

There are 8 functions that can be written out using two-line notation for the given domain and codomain.

Step-by-step explanation:

To write out all functions f : {1, 2, 3} → {a, b} using two-line notation, we need to determine the mapping from each element in the domain to an element in the codomain. Since there are 3 elements in the domain and 2 elements in the codomain, there are 2^3 = 8 possible functions. Here are the functions:

1. f(1) = a, f(2) = a, f(3) = a
2. f(1) = a, f(2) = a, f(3) = b
3. f(1) = a, f(2) = b, f(3) = a
4. f(1) = a, f(2) = b, f(3) = b
5. f(1) = b, f(2) = a, f(3) = a
6. f(1) = b, f(2) = a, f(3) = b
7. f(1) = b, f(2) = b, f(3) = a
8. f(1) = b, f(2) = b, f(3) = b