1.

Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation.

Answer»

P = {set of all triangles in a plane} 

aRb ⇒ a similar to b 

(a) aRa ⇒ every triangle is similar to itself 

∴ aRa is reflexive 

(b) aRb ⇒ if a is similar to b ⇒ b is also similar to a. 

⇒ It is symmetric 

(c) aRb ⇒ bRc ⇒ aRc 

a is similar to b and b is similar to c 

⇒ a is similar to a

⇒ It is transitive 

∴ R is an equivalence relation



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