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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

 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 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

The correct answer is equivalence Relation.
Given aRb, if a is congruent to b,∀a, b∈T.
Then, we have aRa⇒a is congruent to a;
which is always true.
Thus, R is reflexive.
Let aRb⇒a ~ b

b~a

bRa
Thus, R is symmetric.

Let aRb and bRc
a ~ b and b ~ c

a~c

aRc
Thus, R is transitive.
Hence , R is equivalence relation.

Thanks

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