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Question

Let A=2,4,6,8. A relation R on Ais defined by R=2,4,4,2,4,6,6,4. Then R is


A

Antisymmetric

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B

Reflexive

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C

Symmetric

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D

Transitive

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Solution

The correct option is C

Symmetric


Explanation for the correct answer:

Option (C): Symmetric

Given,A=2,4,6,8,R=2,4,4,2,4,6,6,4

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

R=2,4,4,2,4,6,6,4

a,b=2,4,4,2,4,6,6,4Rb,a=4,2,2,4,6,4,4,6R

Therefore, R is symmetric

Explanation for the wrong answer:

Option (A): Antisymmetric

A relation R is not antisymmetric if there exists such that (a,b)R and (b,a)R but ab.

R=2,4,4,2,4,6,6,4

a,b=2,4,4,2,4,6,6,4Rb,a=4,2,2,4,6,4,4,6R

Therefore, R is not antisymmetric

Option (B): Reflexive

A relation is said to be reflexive, if (a,a)R, for everyaA.

R=2,4,4,2,4,6,6,4

Let 2Abut2,2R

Therefore, R is not reflexive

Option (D): Transitive

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

R=2,4,4,2,4,6,6,4

For (a,b)=(2,4)R and (b,c)=4,6R then (a,c)=2,6R

Therefore, R is not Transitive.

Hence, option (C) is the correct answer.


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