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 for all a,b∈T. Then, R is

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Filo · Accepted Answer

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,

n R m \Leftrightarrow m R n

and thus relation R is symmetric .

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

Question Text	Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $a R b$ , if $a$ is congruent to $b$ for all $a, b \in T$ . Then, $R$ is
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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 $a R b$ , if $a$ is congruent to $b$ for all $a, b \in T$ . Then, $R$ is

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