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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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