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Let T be the set of all triangles in the Euclidean plane,

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 ∀ a, b ∈ T. Then R is

(A) reflexive but not transitive

(B) transitive but not symmetric

(C) equivalence

(D) none of these

Solution:

(C) equivalence

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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