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If (R) is an equivalence relation, which statement about (R^{-1}) is correct?यदि (R) समतुल्यता संबंध है, तो (R^{-1}) के बारे में सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: it is also an equivalence relationयह भी समतुल्यता संबंध होगा
Step 1: Since (R) is reflexive, its inverse is also reflexive. Step 2: Since (R) is symmetric, (R^{-1}=R). Step 3: Because (R) is transitive, the same property remains in its inverse.चरण 1: (R) प्रतिवर्ती है, इसलिए उसका प्रतिलोम भी प्रतिवर्ती रहेगा। चरण 2: (R) सममित है, इसलिए (R^{-1}=R) हो जाता है। चरण 3: चूंकि (R) संक्रामी है, वही गुण प्रतिलोम में भी बना रहता है।
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