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

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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