A relation is defined in all the sets containing exactly 2 elements such that R - A - B - A - B is a singleton set then R isA- Reflexive onlyB- Symmetric and transitive onlyC- Symmetric onlyD- Equivalence

The correct option is C Symmetric onlyA ∩ A = A having 2 elements. So, it is not reflexive. A ∩ B = B ∩ A = Singleton set. So, it is symmetric. Let A = 1, 2 ...

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Standard XII

Mathematics

Reflexive Relations

A relation is...

Question

A relation is defined in all the sets containing exactly 2 elements such that $R = {(A, B) : A \cap B$ is a singleton set} then $R$ is

Reflexive only

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Symmetric and transitive only

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Symmetric only

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Equivalence

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Solution

The correct option is C Symmetric only
$A \cap A = A$ having 2 elements. So, it is not reflexive.

$A \cap B = B \cap A$ = Singleton set. So, it is symmetric.

Let
A = {1, 2}
B = {2, 3}
C = {3, 4}
$A \cap B = 2$
$B \cap C = 3$
$A \cap C = ϕ$
So, it is not transitive.

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A relation is defined in all the sets containing exactly 2 elements such that R={(A,B):A∩B is a singleton set} then R is

The correct option is C Symmetric onlyA∩A=A having 2 elements. So, it is not reflexive. A∩B=B∩A = Singleton set. So, it is symmetric. Let A = {1, 2} B = {2, 3} C = {3, 4} A∩B=2 B∩C=3 A∩C=ϕ So, it is not transitive.

A relation is defined in all the sets containing exactly 2 elements such that $R = {(A, B) : A \cap B$ is a singleton set} then $R$ is

The correct option is C Symmetric only
$A \cap A = A$ having 2 elements. So, it is not reflexive.

$A \cap B = B \cap A$ = Singleton set. So, it is symmetric.

Let
A = {1, 2}
B = {2, 3}
C = {3, 4}
$A \cap B = 2$
$B \cap C = 3$
$A \cap C = ϕ$
So, it is not transitive.