Question

Let A be the set of all triangles in the Euclidean plane and R is the relation on A Defined
by ‘a is similar to b’. Then show that R is an equivalence relation on A.

Answer 1

Step-by-step explanation:

Here, A is set of all triangles.

Then, (a,a) ∈ R (Every Triangle is similar to itself)

so, we can say it is Reflexive Relation.......(1)

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(a,b)∈ R [Given]

Then, it's converse is also True.

so, (b,a) ∈ A

Hence, It is also a symnetric Relation..........(2)

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(a,b) ∈ R and (b,c) ∈ R

Then, a must be similar to c

So, (a,c) ∈ R

Hence, we can say it is also a Transitive Relation......(3)

Frome 1 , 2 & 3 we can say that, relation R is Equivalence Relation onn set A.

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Amrit