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 ∀ a, b ∈ T. Then R is ______.

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KollegeApply · Accepted Answer

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 ∀ a, b ∈ T. Then R is equivalence. Explanation: Given aRb, if a is congruent to b, ∀ a, b ∈ T. Then, we have aRa ⇒ a is congruent to a; which is always true. So, R is reflexive. Let aRb ⇒ a ~ b b ~ a bRa So, R is symmetric. Let aRb and bRc a ~ b and b ~ c a ~ c aRc So, R is transitive. Therefore, R is equivalence relation.

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