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If (R) and (S) are two symmetric relations on (A), which statement is always true?यदि (R) और (S), (A) पर दो सममित संबंध हैं, तो कौन सा कथन हमेशा सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (R \cap S) is symmetric(R \cap S) सममित है
Step 1: If ((a,b) \in R \cap S), then the pair lies in both (R) and (S). Step 2: Since both are symmetric, ((b,a)) lies in both. Step 3: Therefore, ((b,a) \in R \cap S), so intersection preserves symmetry.चरण 1: यदि ((a,b) \in R \cap S), तो ((a,b)) दोनों संबंधों में होगा। चरण 2: दोनों सममित हैं, इसलिए ((b,a)) भी दोनों में होगा। चरण 3: अतः ((b,a) \in R \cap S); प्रतिच्छेद पर सममिति सुरक्षित रहती है।
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