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Which of the following relation is both reflexive and an identity relation in set A = {a.b} from A\rightarrow A ?

  • Option 1)

    \left \{ (a,b);(a,a);(b,b) \right \}

  • Option 2)

    \left \{ (a,a);(b,b) \right \}

  • Option 3)

    \left \{ (a,b);(b,a);(a,a);(b,b) \right \}

  • Option 4)

    All of the above

 

Answers (1)

best_answer

As we have learnt,

 

Identity Relation -

If every element of A is related to itself only.

- wherein

I_{A}=\{ (A,A):a\epsilon A\}

 

 Though all the above are reflexive relation but only {(a,a); (b.b)} is an identity relation.

 


Option 1)

\left \{ (a,b);(a,a);(b,b) \right \}

Option 2)

\left \{ (a,a);(b,b) \right \}

Option 3)

\left \{ (a,b);(b,a);(a,a);(b,b) \right \}

Option 4)

All of the above

Posted by

Himanshu

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