When S is a nonempty set, a function f:S×S→S is called a binary operation.
Each ordered pair (a,b)Є(S×S) is associated to a unique element f(a,b) in S.
Examples: addition of a and b (both natural numbers). a+b is also a natural number.
a belongs to N, b belongs to N, and a+B also belongs to N.
Commutative binary operation
Associative binary operation
Distributive binary operation