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  • Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 16 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 16 Maths Textbook Solution

Answers (1)

Answer:R\cup S\: is\: not\: transitive
Hint:  For transitive relation
x=y \: and\: y=z, then\: also\: x=z.
Given:\\\text{R and S are transitive relation on a set A}
To Prove:R\cup S\: \text{ may not be a transitive relation on A}
Explanation:
We will prove this by means of an example.
Let \: A=\left \{ a, b, c \right \} be\: a\: set
R= \left \{ (a,a),(b, b),(c, c),(a,b),(b, a)\right \} and
S=\left \{ (a, a),(b, b),(c,c),(b, c),(c, b) \right \} are\: two\: relations\: on\: A
\\\text{Clearly, R and S are transitive relation on A.}       
Now, R\cup S=\left \{ (a, a),(b, b),(c, c),(a, b),(b, a),(b, c),(c, b) \right \}
Here, (a, b) \: \epsilon \: R\cup S\: and \: (b, c)\: \epsilon\: R\cup S
but \: (a,c) \: \notin\: R\cup\: S
R\cup S\: is\: not\: transitive

 

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