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  • Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 11 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 11 Maths Textbook Solution.

Answers (1)

Answer: R is an equivalence relation on A
Hint: To prove equivalence relation it is necessary that the given relation should be reflexive, symmetric and transitive.
Given: O\; be\; the\; origin\; and\; R=\left \{ \left (P, Q \right ):OP=OQ \right \} be\; a\; relation \; on\; A \; where\; O\; is \; the\; origin.
Explanation:
Let A be a set of points on a plane.
Reflexivity:
Let\: P \: \epsilon \: A
Since, OP=OP=(P, P) \: \epsilon \: R
R is reflexive.
Symmetric:
Let (P, Q) \: \epsilon \: R \: f\! or\: P, Q \: \epsilon \: A
Then \: OP=OQ
  OQ=OP
(Q, P) \: \epsilon \: R
R is symmetric
Transitive:
Let (P, Q) \: \epsilon \: R\: and\: (Q, S) \: \epsilon \: R
OP=OQ \: \: ...(i)\: and \: \: OQ=OS \: \:....(ii)
Putting  (ii) in (i), we get
OP=OS
(P, S)\: \epsilon \: R
R is transitive
Therefore, R is reflexive, symmetric and transitive.
Thus, R is an equivalence relation on A.

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