Question

prove that if A is the set of the members of a family and R means " is brother of " then it is a transitive relation ??​

Answer 1

SOLUTION

TO PROVE

If A is the set of the members of a family and R means " is brother of " then it is a transitive relation

EVALUATION

Here the given set is A is the set of the members of a family

Now the relation R is defined by R means " is brother of "

Let a , b , c ∈ A such that

(a, b) ∈ R and (b, c) ∈ R

⇒a is brother of b and b is brother of c

⇒a is brother of c

⇒(a, c) ∈ R

Thus (a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R

Hence R is transitive relation

Hence proved

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Answer 2

Answer:

SOLUTION

TO PROVE

If A is the set of the members of a family and R means " is brother of " then it is a transitive relation

EVALUATION

Here the given set is A is the set of the members of a family

Now the relation R is defined by R means " is brother of "

Let a , b , c ∈ A such that

(a, b) ∈ R and (b, c) ∈ R

⇒a is brother of b and b is brother of c

⇒a is brother of c

⇒(a, c) ∈ R

Thus (a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R

Hence R is transitive relation

Hence proved