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Let R = {(3,3),(5,5),(9,9),(12,12),(5,12),(3,9), (3,... | Relation (Mathematics) | DivineJEE

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Mathematics

JEE Mains (Online 2013)

Mathematics

Let

R = \{(3,3),(5,5),(9,9),(12,12),(5,12),(3,9)

,

(3,12),(3,5)\}

be a relation on the set

A = \{ 3,5,9,12\}

. Then,

R

is

A

reflexive, symmetric but not transitive\\

B

symmetric, transitive but not reflexive\\

C

an equivalence relation\\

D

reflexive, transitive but not symmetric\\

Correct Answer:

D

Explanation

(d) : Let

R = \{(3,3),(5,5),(9,9),(12,12),(5,12)

,

(3,9),(3,12),(3,5)\}

be a relation on the set

A = \{ 3,5,9,12\}

Clearly, every element of A is related to itself. Therefore, it is a reflexive. Now,

R

is not symmetric because 3 is related to 5 but 5 is not related to 3. Also,

R

is transitive relation because it satisfies the property, if

aRb

and

bRc

, then

aRc

.

Select an option to instantly check whether it is correct or wrong.

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