Friday, December 19, 2008

Binary Operations and Types of Binary Operations

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

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