Can you explain if you fulfill this example with a function.

Question

Example

If I have a function with the elements of the image. domain: 1,2,3. codomain: a, b. but they don't have pointers or arrows between them, is that a function?

Answer 1

As it is, these are just two sets. A function is a rule that relates these two sets. Given these two sets, there are a lot of functions you can define so to relate them. For example, you can take $f(1) = a$, $f(2) = b$ and $f(3) = a$ or $f(1) = b$, $f(2)=a$, $f(3) = a$ or even $f(1)=f(2)=f(3)=a$. What you cannot do is to relate an element of the domain ($\{1,2,3\}$ in your case) to more than one element on the codomain ($\{a,b\}$) in your case.