# discrete 5.4

For any nonempty sets 𝐴, 𝐵,

any function **𝑓:𝐴×𝐴→𝐵 is called a binary operation on 𝐴.**.

If 𝐵⊆𝐴, then the binary operation is said to be closed.

## commutative
f(a,b) = f(b,a)
## associative
f(a,f(b,c)) = f(f(a,b),c)
## identity

f(x,a) = f(a,x) = a