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If (R) is a transitive relation, which statement about (R\circ R) is always true?यदि (R) संक्रामी संबंध है, तो (R\circ R) के बारे में कौन सा कथन हमेशा सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (R\circ R\subseteq R)(R\circ R\subseteq R)
Step 1: ((a,c)\in R\circ R) means there is some (b) such that ((a,b)\in R) and ((b,c)\in R). Step 2: Since (R) is transitive, ((a,c)\in R). Step 3: Hence (R\circ R\subseteq R).चरण 1: ((a,c)\in R\circ R) का अर्थ है कि कोई (b) है जिसके लिए ((a,b)\in R) और ((b,c)\in R)। चरण 2: (R) संक्रामी है, इसलिए ((a,c)\in R)। चरण 3: इसलिए (R\circ R) हमेशा (R) का उपसमुच्चय होगा।
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