Q. 32

# Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a R b if a is congruent to b for all a, b ϵ T. Then, R isA. reflexive but not symmetricB. transitive but not symmetricC. equivalenceD. none of these

R: a R b a b

Since, every triangle aT is congruent to itself, therefore (a, a)R aT. Hence, R is reflexive.

If a b, then b a. Hence if (a, b)R, then (b, a)R a, bT. Hence, R is symmetric.

If a b and b c, then a c. Hence if (a, b) and (b, c) belongs to R, then (a, c) will belong to R a, b, cT. Hence, R is transitive.

Since R is reflexive, symmetric and transitive, therefore R is equivalence relation.

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