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Consider the following two binary relations on the s... | Relation (Mathematics) | DivineJEE

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Mathematics

JEE Mains (Online 2018)

Mathematics

Consider the following two binary relations on the

setA = \{ a,b,c\}

:\\

R_{1} = \{(c,a),(b,b),(a,c),(c,c),(b,c),(a,a)\}

and

R_{2} = \{(a,b),(b,a),(c,c),(c,a),(a,a),(b,b),(a,c)\}

. Then

A

R_{1}

is not symmetric but it is transitive\\

B

both

R_{1}

and

R_{2}

are transitive\\

C

R_{2}

is symmetric but it is not transitive\\

D

both

k_{1}

and

k_{2}

, are not symmetric

Correct Answer:

C

Explanation

(c) :

R_{2}

is symmetric but

R_{2}

is not transitive as

(c,a),(a,b) \in R_{2}

but

(c,b) \notin R_{2}

.

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