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

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.