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.
Example:
(i) Squaring number; 2 ² =4
(ii) Cube roots of unity of a number ; 3 ³ = 27
What is 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.
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