Question

lets A be the set consisting of all the members of a family .the reaction R defined"aRb"if a is not a sister of b​

Answer 1

Step-by-step explanation:

The relation R defined on a non-empty set consisting of children in a family is not reflexive.

Since a can't be brother of a so (a,a)



∈R for any a belonging to the family.

This relation is not symmetric as if (a,b)∈R then (b,a)



∈R as if a is brother of b this means b can be sister of a for any a,b belonging to the family.

But this relation is also transitive as if a is brother of b and b is brother of c then certainly a is brother of c i.e. (a,b)∈R,(b,c)∈R⇒(a,c)∈R for all a,b,c belonging to the family.

So the relation is not symmetric but transitive.