#### Need solution for RD Sharma maths Class 12 Chapter Relation Exercise 1.1 Question 5 Subquestion (i) 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 : $a R b \text { if } a-b>0$

Solution :

Reflexivity:

Let $a$ be an arbitrary element of $R$

Then,$a \in A$

But  $a-a=0 \ngtr 0$

So, this relation is not reflexive.

Symmetry :

Let

\begin{aligned} &(a, b) \in R \\ &a-b>0 \\ &-(b-a)>0 \\ &b-a<0 \end{aligned}

So, the given relation is not symmetric.

Transitivity :

\begin{aligned} &\text { Let }(a, b) \in R \; {\text {and }}(b, c) \in R \\ &\text { Then, } a-b>0 \; \; \; \; \; \; \; ...(i)\\ &\; \; \; \; \qquad b-c>0 \; \; \; \; \; \; \;...(ii) \end{aligned}

Adding eq (i) & (ii), we get

\begin{aligned} &a-b+b-c>0 \\ &a-c>0 \\ &(a, c) \in R \end{aligned}

So, the given relation is transitive.