Let R be the relation in the set N given by R={(a,b):a=b−2,b>6}.Choose the correct answer.(A)(2,4)∈ R(B)(3,8)∈R(C)(6,8∈R(D)(8,7)∈R

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Types of Relation

TYPES OF RELATION

Empty Relation

Relation is said to be empty relation if no element of set X is related or mapped to any element of X i.e, R = Φ.

Universal Relation

A relation R in a set, say A is a universal relation if each element of A is related to every element of A.

R = A × A.

Identity Relation

Every element of set A is related to itself only then the relation is identity relation.

Inverse Relation

Let R be a relation from set A to set B i.e., R ∈ A × B. The relation R^-1 is said to be an Inverse relation if R^-1 from set B to A is denoted by R^-1

Reflexive Relation

If every element of set A maps to itself, the relation is Reflexive Relation. For every a ∈ A, (a, a) ∈ R.

Symmetric Relation

A relation R is said to be symmetric if (a, b) ∈ R then (b, a) ∈ R, for all a & b ∈ A.

Transitive Relation

A relation is said to be transitive if, (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R, for all a, b, c ∈ A

Equivalence Relation

A relation is said to be equivalence if and only if it is Reflexive, Symmetric, and Transitive.

	LIST I		LIST II
A.	Range of y=cosec^-1x	I.	R-(-1, 1)
B.	Domain of sec^-1x	II.	(0, π)
C.	Domain of sin^-1x	III.	[-1, 1]
D.	Range of y=cot^-1x	IV.	\([\frac{-π}{2},\frac{π}{2}]\)-{0}

Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer. (A) (2, 4) ∈ R (B) (3, 8) ∈R (C) (6, 8) ∈R (D) (8, 7) ∈ R

Solution and Explanation

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