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Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 13 Maths Textbook Solution.

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Answer:  Hence prove, S is not an equivalence relation on R.
Hint:  To prove an equivalence relation it is necessary that the given relation should be reflexive, symmetric and transitive.
Given: S\left \{ \left ( a, b \right ):a^{2}+b^{2}=1 \right \}  
Let \: a=\frac{1}{2} \, \epsilon \, R
Then, a^{2}+a^{2}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\neq 1
(a, a) \notin S
S is not reflexive.
When one the three properties are not valid, relation not an equivalence.
Hence, S is not an equivalence relation on R.

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