Mark the correct alternative in the following question: Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b ∈ T. Then, R is ____________ .

Question

KollegeApply · Accepted Answer

We have, R = {(a, b) : a is congruent to b; a, b ∈ T} As, a ≅ a ⇒ (a, a) ∈ R So, R is reflexive relation Let (a, b) ∈ R. Then, a ≅ b ⇒ b ≅ a ⇒ (b, a) ∈ R So, R is symmetric relation Let (a, b) ∈ R and (b, c) ∈ R. Then, a ≅ b and b ≅ c ⇒ a ≅ c ⇒ (a, c) ∈ R So, R is transitive relation ∴ R is an equivalence relation Hence, R is equivalence.

AChoose Your Answer