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

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

Answers (1)

Answer : Symmetric

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=10, x, y \in N(x, y) \in\{(9,1),(1,9),(2,8),(8,2),(3,7),(7,3),(4,6),(6,4),(5,5)\}

Solution :

This is not reflexive as  (1,1),(2,2) \ldots \ldots are absent.

This only follows the condition of symmetry as (1,9) \in R \operatorname{also}(9,1) \in R

This is not transitive because \{(1,9),(9,1)\} \in R \text { but }(1,1) is absent.

Hence, this relation is not satisfying reflexivity and transitivity.

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