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Need solution for RD Sharma maths Class 12 Chapter Relation Exercise 1.1 Question 5 Subquestion (i) maths textbook solution.

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Answer: Given relation is transitive


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 :


  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 :


\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.

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