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  • Stuck here, help me understand: Which of the following relation is anti - symmetric relation ?

Which of the following relation is anti - symmetric relation ?

 

  • Option 1)

    \left \{ \left ( 1,2 \right )\left ( 2,3 \right )\left ( 3,2 \right ) \right \}

     

     

     

  • Option 2)

    \left \{ \left ( 1,2 \right )\left ( 2,2 \right )\left ( 3,1 \right )\left ( 1,3 \right )\left ( 2,1 \right ) \right \}

  • Option 3)

    \left \{ \left ( 1,1 \right )\left ( 2,2 \right ) \right \}

  • Option 4)

    \left \{ \left ( 1,2 \right )\left ( 2,1 \right ) \right \}

 

Answers (1)

best_answer

As we learned 

 

Anti - Symmetric Relation -

\left ( a,b \right )\in R \: and \: \left ( b,a \right )\in R\Rightarrow a=b

Here, R is relation in A

-

 

 Since (1,2) is present (2,1) should be there.

 


Option 1)

\left \{ \left ( 1,2 \right )\left ( 2,3 \right )\left ( 3,2 \right ) \right \}

 

 

 

Option 2)

\left \{ \left ( 1,2 \right )\left ( 2,2 \right )\left ( 3,1 \right )\left ( 1,3 \right )\left ( 2,1 \right ) \right \}

Option 3)

\left \{ \left ( 1,1 \right )\left ( 2,2 \right ) \right \}

Option 4)

\left \{ \left ( 1,2 \right )\left ( 2,1 \right ) \right \}

Posted by

Himanshu

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