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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. |
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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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