Let R be the relation in the set N given by R={\((a,b):a=b−2,b>6\)}.Choose the correct answer
\((2,4)∈ R\)
\((3,8)∈R\)
\((6,8)∈R\)
\((8,7)∈R\)
The Correct Option is C
Solution and Explanation
\(R = {(a, b): a = b − 2, b > 6}\)
Now, since \(b > 6, (2, 4) ∉ R\)
Also, as \(3 ≠ 8 − 2, (3, 8) ∉ R\)
And, as 8\(≠ 7 − 2 (8, 7) ∉ R\)
Now, consider \((6, 8).\) We have \(8 > 6\)
and also, \(6 = 8 − 2. ∴(6, 8) ∈ R\)
The correct answer is C.
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Concepts Used:
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.