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.
Types
Commutative binary operation
Associative binary operation
Distributive binary operation
Showing posts with label Binary operations. Show all posts
Showing posts with label Binary operations. Show all posts
Friday, December 19, 2008
Friday, November 7, 2008
JEE Mathamatics Study Guide 4. Binary Operations - Revision Facilitator
4.1 Binary operations
4.2 Types of binary operation
4.3 Identity and inverse elements
4.4 Composition table
Study Plan
Day 1
4.1 Binary operations
4.2 Types of binary operation
Day 2
4.3 Identity and inverse elements
4.4 Composition table
Day 3
Objective type exercises 1 to 12
True/false type exercises 1 to 9
4.2 Types of binary operation
4.3 Identity and inverse elements
4.4 Composition table
Study Plan
Day 1
4.1 Binary operations
4.2 Types of binary operation
Day 2
4.3 Identity and inverse elements
4.4 Composition table
Day 3
Objective type exercises 1 to 12
True/false type exercises 1 to 9
Saturday, June 7, 2008
Ch. 4. Binary Operations - 1
Binary operation
Let S be a non-void set. A function from S×S to S is called a binary operation on S.
f:S×S S is binary operation on set S
A binary function f on a set S×S associates each order pair (a,b) of elements of S×S to a unique element f(a,b) of S.
Instead of writing f(a,b) for the image of an ordered pair we can write a f b.
a f b = f(a,b)
Binary operations are represented by the symbols *, etc. instead of letter f,g etc.
Instead S×S only Set S is mentioned in binary operation but it is to be understood as S×S.
Thus a binary operation * on a set S associates each ordered pair (a,b) of elements of S to a unique element a*b of S. (a*b is an element in S that is obtained by the relation a*b -- * represents relation on set S and set S)
Example: Addition of two natural numbers.
(a,b) is an element of N×N (a and b are natural numbers)
a+b is also a natural number and is also an element of N.
Addition of natural numbers is f:N×NN a binary operation.
Types of binary operations
Commutative binary operation.
Associative binary operation.
Distributive binary operation
Identity and inverse elements
Identity element
Inverse of an element
Composition table
A binary operation on finite set can be completely described by means of a table known as a composition table.
Let S be a non-void set. A function from S×S to S is called a binary operation on S.
f:S×S S is binary operation on set S
A binary function f on a set S×S associates each order pair (a,b) of elements of S×S to a unique element f(a,b) of S.
Instead of writing f(a,b) for the image of an ordered pair we can write a f b.
a f b = f(a,b)
Binary operations are represented by the symbols *, etc. instead of letter f,g etc.
Instead S×S only Set S is mentioned in binary operation but it is to be understood as S×S.
Thus a binary operation * on a set S associates each ordered pair (a,b) of elements of S to a unique element a*b of S. (a*b is an element in S that is obtained by the relation a*b -- * represents relation on set S and set S)
Example: Addition of two natural numbers.
(a,b) is an element of N×N (a and b are natural numbers)
a+b is also a natural number and is also an element of N.
Addition of natural numbers is f:N×NN a binary operation.
Types of binary operations
Commutative binary operation.
Associative binary operation.
Distributive binary operation
Identity and inverse elements
Identity element
Inverse of an element
Composition table
A binary operation on finite set can be completely described by means of a table known as a composition table.
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