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A relation (R) on a set (A) is symmetric. If ((4,7) \in R), what must definitely be true?किसी समुच्चय (A) पर (R) सममित है। यदि ((4,7) \in R), तो निश्चित रूप से क्या सत्य होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ((7,4) \in R)((7,4) \in R)
Step 1: The definition of a symmetric relation says that ((b,a)) must be present whenever ((a,b)) is present. Step 2: Since ((4,7)) is given, ((7,4)) must be present. Step 3: Symmetry does not automatically force diagonal pairs.चरण 1: सममित संबंध की परिभाषा सीधे कहती है कि ((a,b)) के साथ ((b,a)) भी होगा। चरण 2: यहाँ ((4,7)) दिया है, इसलिए ((7,4)) अवश्य होगा। चरण 3: सममितता से विकर्ण युग्म अपने आप नहीं मिलते।
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