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Consider the non-empty set consisting o...

Consider the non-empty set consisting of children in a family and a relation R defined as aRb, if a is brother of b. Then, R is

A

Symmetric but not transitive

B

Transitive but not transitive

C

Neither symametic nor transitive

D

Both symmetric and transitive

Text Solution

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The correct Answer is:
B
a cannot be a brother of a
`:. (a,a)notin RAAaepsiA`
so, R is not reflexive
`(a,b) epsi RrArr` a is brother of b but b may not be a brother of a.
i.e., may be sister of a `" " :. (b,a)notinR`
`" " :.` R is not symmetric
Let (a,b) `epsi` Rand (b,c)rpsiRrArr(a,c)`epsiR`
so, R is transitive
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