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If (R) and (S) are both transitive relations, which statement about (R \cap S) is correct?यदि (R) और (S) दोनों संक्रामी संबंध हैं, तो (R \cap S) के बारे में कौन-सा कथन सही है?
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Correct answer:सही उत्तर: (R \cap S) is always transitive(R \cap S) हमेशा संक्रामी होता है
Step 1: If ((a,b)) and ((b,c)) are in (R \cap S), they are in both (R) and (S). Step 2: Since both relations are transitive, ((a,c)) is in both. Step 3: Therefore, ((a,c)) is in (R \cap S), so the intersection is transitive.चरण 1: यदि ((a,b)) और ((b,c)) दोनों (R \cap S) में हैं, तो वे (R) और (S) दोनों में होंगे। चरण 2: दोनों संक्रामी हैं, इसलिए ((a,c)) भी दोनों में होगा। चरण 3: अतः ((a,c)), (R \cap S) में होगा।
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