Let R -3-3-6-6-9-9-12-12-6-12-3-9-3-12-3-6be a relation on the set A -3-6-9-12- The relation isA- An equivalence relationB- Reflexive onlyC- Reflexive and transitive onlyD- Reflexive and symmetric only

The correct option is C Reflexive and transitive only A = 3,6,9,12 and (3,3),(6,6),(9,9),(12,12)∈ R ⇒ R is reflexive (6,12)∈R but (12,6) ∉ R ⇒ R is not a symme ...

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Byju's Answer

Standard XII

Mathematics

Definition of Sets

Let R =3,3,6,...

Question

Let R={(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}

be a relation on the set A={3, 6, 9, 12}. The relation is

Reflexive and symmetric only

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An equivalence relation

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Reflexive only

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Reflexive and transitive only

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Solution

The correct option is D
Reflexive and transitive only

A = {3,6,9,12} and (3,3),(6,6),(9,9),(12,12) $\in$ R $\Rightarrow$ R is reflexive

(6,12) $\in$ R but (12,6) $\notin$ R $\Rightarrow$ R is not a symmetric whereas given R is clearly transitive

Suggest Corrections

Similar questions

Q. Let R = {(3, 3), (6, 6), (9, 9), (3, 6), (3, 12), (6, 12), (3, 9), (12, 12)} be a relation on the set A = {3, 6, 9, 12}. Then the relation is

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, R is

Q. Let

R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}

be a relation on the set

A = {3, 6, 9, 12}

. The relation is

Q. Let

N

denote the set of natural numbers and

R

be a relation on

N \times N

defined by

(a, b) R (c, d) ⟺ a d (b + c) = b c (a + d) .

Then on

N \times N, R

Q. Let

R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}

be a relation on the set

A = {3, 6, 9, 12} .

Then the relation is

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Let R={(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A={3, 6, 9, 12}. The relation is

The correct option is D Reflexive and transitive only A = {3,6,9,12} and (3,3),(6,6),(9,9),(12,12)∈ R ⇒ R is reflexive (6,12)∈R but (12,6) ∉ R ⇒ R is not a symmetric whereas given R is clearly transitive

Let R={(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}

be a relation on the set A={3, 6, 9, 12}. The relation is

The correct option is D
Reflexive and transitive only

A = {3,6,9,12} and (3,3),(6,6),(9,9),(12,12) $\in$ R $\Rightarrow$ R is reflexive

(6,12) $\in$ R but (12,6) $\notin$ R $\Rightarrow$ R is not a symmetric whereas given R is clearly transitive