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  • Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 15 Subquestion (ii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 15 Subquestion (ii) Maths Textbook Solution.

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Given:Hence \: proved, R\cup S\: is \: re\! flexive.
Hint:(a, a) \, \epsilon \, R \, \forall\, a \, \epsilon\, X\, or\, as\, I \subseteq R \ , \text{where, I, is the identity relation on A.}
Explanation:
Given:   R and S are two relations on A such that R is reflexive.
To Prove:R\cup S\: is\: re\! f\! lexive.
Suppose \: R\cup S\: is\: not\: re\! f\! lexive.
\\\text{This means that there is and }R\cup S\: \text{ such that }(a, a) \: \notin\: R\cup S       
Since, a \, \epsilon \: R\cup S,
a \: \epsilon \: R \: or \: a\: \epsilon \: S
I\! f \: a \: \epsilon \: R, then (a, a) \: \epsilon \: R [R\: is\: re\! flexive]
(a,a) \: \epsilon \: R\cup S
Hence, R\cup S\: is \: re\! flexive.

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