Binary Operations

Binary Operations are as given below,

• Commutative Law
• Associative Law

Let S be any non-empty set. An operation * is called a binary operation on S if " a, b Î S a * b Î SLet S be any non-empty set. An operation * is called a binary operation on S if " a, b Î S a * b Î S

Example:

(1) '+' is a binary operation on the set of naturals.

(2) '.' is a binary operation on the set of naturals.

(iv) Addition, subtraction and multiplication are binary operations on I.

Commutative law

Let * be a binary operation on the set S. * is said to be associative in S if " a, b Î S a * b =b * a

Associative law

Note:

(1) '+' & '.' are commutative and associative in the sets, N, I, Q, Q^|, R and C.

i.e, a + b = b + a

and a.b = b.a

a + (b + c) = (a + b) + c