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


Now,


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


bRa


(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


aRc


(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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