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Relation of Sets

A relation

It may be noted that, here

If the set

Further, if

In case,

We notice that the following ordered pairs have the property

Hence

We also notice that

**R**consists of the followings:**(i)**Two sets say**A**and**B (ii)**an open sentence**P(x, y)**in which**P(a, b)**is either true or false for any ordered pair**(a, b)****A × B**, then**R**is called a relation from**A**to**B**and is denoted by**R = {A, B, P(x, y)}**.It may be noted that, here

**R**does not stand for the set of real numbers.**Relation R in a set**If the set

**B = A**, then the relation**R**is said to be defined in the set**A**or**R**is a relation in the set A and**R = {A, A, P(x, y)}.**Further, if

**P(a, b)**is true we say that “**a**is related to**b**in the sense of**R**” and is written as**aRb**.In case,

**P(a, b)**is not true we say that**a**is not related to**b**in the sense of**R**and is written as**a R b**.**Illustration 1: let A = {1, 2, 3} ; B = {1, 6}**and**P (x, y) = x**is less than**y**, then**A × B = {(1, 1), (1, 6), (2, 1), (2, 6), (3, 1), (3, 6)}**.We notice that the following ordered pairs have the property

**x < y**,**(1, 6), (2, 6) and (3, 6).**Hence

**R = {(1, 6), (2, 6), (3, 6)}.**We also notice that

**R**is a subset of**A × B**.**A relation**

Definition of relation:Definition of relation:

**R**from a set**A**to the set**B**is a subset of**A × B**i.e.**R ⊆ A × B**.**Services: -**Relation of Sets Homework | Relation of Sets Homework Help | Relation of Sets Homework Help Services | Live Relation of Sets Homework Help | Relation of Sets Homework Tutors | Online Relation of Sets Homework Help | Relation of Sets Tutors | Online Relation of Sets Tutors | Relation of Sets Homework Services | Relation of SetsSubmit Your Query ???

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Topics

Real Number Absolute Value
Addition Of Matrices
Square Matrix Adjoint
Algebraic Structures
Alternating Series
Linear Equations Determinants
Archimedean Real Numbers
Binary Operation
Binary Relation In A Set
Bounded, Unbounded Sets
Cauchy Root Test
Caylay Hamiltion Theorem
Circular Permutation
Common Roots
Complex Numbers
Complex Number Conjugate
Conjugate Of A Matrix
Constant Sequences
Convergence Of A Sequence
Cosets
Cubic, Biquadratic Equations
De Moivre Theorem
Real Number Denseness
Order 3 Determinants
Differences Of Matrices
Direct Sum Of Vector Subspaces
Eigen Vector
Elementary Matrices
Matrix Elem. Transformations
Equal Matrices
Equal Roots
Two Permutations Equity
Equivalent Matrices
Trigonometry Function Expansion
Field
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Algebra Fundamental Theorem
Gaussian Integer
Geometric Series
Group
Ideals
Quantity Increasing Roots
Infinite Series Convergent
Integers
Inverse Of Square Matrix
Inverses Of Elementary Matrices
Iota, Imaginary Numbers
Left-Right Identity
Sequence Limit Points
Linear Combination Vectors Span
Linear Dependence, Independence
Linear Homogeneous Equations
Two Subspaces Linear Sum
Matric Polynomial
Matrix
Linear Equation Matrix Inverse
Matrix Multiplication
Matrix Scalar Multiplication
Method Of Difference
Minors And Co-factors
Multiplication Modulo P
Normal Sub-Group
Normalizer Or Centalizer
Orbit Of Permutation
Peano Axioms
Permutation Function
Pigeon Hole Principle
Matrices Integral Powers
Mathematical Induction Principal
Two Determinants Product
Two Permutations Product
Properties Of Modulus
Rank Of A Matrix
Rational Numbers
Rational, Integral Polynomial
Reciprocal Roots
Relation Of Sets
Rings Of A Set
Row By Column Matrix
Sequence
Series
Series Of Positive Terms
Series Partial Sum Sequence
Subrings
Sum Of A Series
Cosine Series Sum
Sum Of Sine Series
Symmetric/Skew Symm. Matrices
Roots Symmetric Functions
Symmetric Set Degree N
Synthetic Division
Transformation In General
Transformations Of Equations
Transpose Of A Matrix
Matrix Transposed Conjugate
Transposition
Complex Numbers Representation
Vector Space
Vector Sub-spaces
Whole Numbers
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