Define binary operation

Residue classes Modulo n

An operation which is performed on two number and resultant values is another number of the same system is called binary operation. For Example 3 + 4 = 7 . here + is a binary operation.Define binary operation on 7, 8 under multiplication example is that 7 × 8 = 56  here multiplication is binary operation.

Second definition of binary operation:

Let G be a non empty set, then binary operation on G (  is a function) denoted by ⋇ ( read as star)

Defined as ;Define binary operation by symbolically;

⋇ : G × G → G

That is

for all a , b ∈ G  this implies that  a ⋇ b ∈ G.

Remember that;

If ⋇ is binary operation on G is said to be closed under binary operation ⋇ ( star).

Define unary operation:

A solution which is performed on a single number and its results another number of the same system or of a different system is called a unary operation.


(i) Squaring number;  2 ² =4

(ii) Cube roots of unity of a number ; 3 ³ = 27

What is Residue classes Modulo n.

Residue classes Modulo n

Let N and n be any two natural number with N ≥ n . When n is divided by n then the reminder can be 0 , 1 , 2 , 3 ,4…………., (n – 1).

The set { 0, 1, 2 ,3 ,4……..,(n – 1) } of all reminders is called residue class modulo n.


unit and unity ring theory

Fourth roots of unity power

Cube root of unity power

Cartesian product of two set