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Provide solution for RD Sharma Class 12 Chapter Relation Exercise 1.1 Question 18 Subquestion (iii) Maths textbook solution.

Answers (1)

Answer : Symmetric, Reflexive and transitive

Hint :

A relation R on set A is

Reflexive relation:

If  (a, a) \in R for every a \in A

Symmetric relation:

If (a,b) is true then (b,a)  is also true for every a, b \in A

Transitive relation:

If  (a,b) and (b, c) \in R then (a, c) \in R  for every a, b, c \in A

Given :

x y \text { is square of an integer } \ x, y \in N

(x, y) \in\{(1,1),(2,2),(4,1),(1,4)(3,3),(9,1),(1,9),(4,4),(2,8),(8,2),(16,1),(1,16) \ldots\}

Solution :

This is reflexive as  (1,1),(2,2) \ldots \ldotsare present.

This is also symmetric because a R b \Leftrightarrow b R a \text { for all } a, b \in N

This is transitive because if  a R b \text { and } b R c \Leftrightarrow a R c \ \ \ a, b, c \in N

This relation is reflexive, symmetric, and transitive.

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