Question

Is union of two transitive relations transitive? Justify.​

Answer 1

SOLUTION

TO CHECK

Is union of two transitive relations transitive? Justify

EVALUATION

No union of two transitive relations is not necessarily transitive

For example let us assume two transitive relation R and S on the set A = { 1 , 2 , 3 , 4 }

R = { (1,2) , ( 2,3) , (1,3) }

S = { (2,3) , (3,4) , (2,4) }

Clearly both R and S are transitive

Now (1,2) , (2,4) ∈ R ∪ S but (1, 4) ∉ R ∪ S

Thus R ∪ S is not transitive

Hence we can conclude that the union of two transitive relations is not necessarily transitive

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