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 isA. reflexive but not transitiveB. transitive but not symmetricC. equivalenceD. none of these

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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