Question

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

Answer 1

Correct Answer - 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