Q

# Help me understand! - Sets, Relations and Functions - JEE Main

Let $\dpi{100} R= \left \{ \left ( 3,3 \right ) \left ( 6,6 \right ),\left ( 9,9 \right )\left ( 12,12 \right )\left ( 6,12 \right )\left ( 3,9 \right ),\left ( 3,12 \right )\left ( 3,6 \right )\right \}$

be a relation on the set  $\dpi{100} A=\left \{ 3,6,9,12 \right \}$ The relation is

• Option 1)

reflexive and symmetric only

• Option 2)

an equivalence relation

• Option 3)

reflexive only

• Option 4)

reflexive and transitive only.

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As we learnt in

Equivalence Relation -

A relation which is reflexive, symmetric & transitive is called Equivalence Relation.

-

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

A = {3, 6, 9, 12}

Now, $(6, 12)\epsilon R$  but $(6, 12) \not \epsilon R$ so it is not symmetric.

Now $(6, 12)\epsilon R$

$(12, 12)\epsilon R$

So $(6, 12)\epsilon R$ so it is transitive.

Correct option is 4.

Option 1)

reflexive and symmetric only

This is an incorrect option.

Option 2)

an equivalence relation

This is an incorrect option.

Option 3)

reflexive only

This is an incorrect option.

Option 4)

reflexive and transitive only.

This is the correct option.

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