Q. 28

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

Answer :

Given that,

R be a relation on T defined as aRb if a is congruent to b a, b T


aRa a is congruent to a, which is true since every triangle is congruent to itself.

(a,a) R a T

R is reflexive.

Let aRb a is congruent to b

b is congruent to a


(a,b) R (b,a) R a, b T

R is symmetric.

Let aRb a is congruent to b and bRc b is congruent to c

a is congruent to c


(a,b) R and (b,c) R (a,c) R a, b,c T

R is transitive.

Hence, R is an equivalence relation.

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