Question

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 congruent to b∀ a,b belong to T then R is ​

Answer 1

Answer:

equivalence

Step-by-step explanation:

Let there be three triangles a,b,c in Euclidean plane such that aRb and bRc.

We know that if triangle a is congruent to triangle b and triangle b is congruent to triangle c, triangle a must also be congruent to triangle c .

So, aRc and thus relation R is transitive .

Also we know that any triangle (say t) in Euclidean plane is always congruent to itself .

So, tRt and thus relation R is reflexive .

Let there be two triangles n and m in Euclidean plane.

We know that if n is congruent to m, m must also be congruent to n.

So, nRm⇔mRn and thus relation R is symmetric .

Thus, finally we arrive at conclusion that realation R is equivalence relation .

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