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If (R) is symmetric, what can be said about the complement of (R) with respect to (A\times A)?यदि (R) सममित है, तो (A\times A) के सापेक्ष (R) का पूरक कैसा होगा?
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Correct answer:सही उत्तर: The complement will also be symmetricपूरक भी सममित होगा
Step 1: If ((a,b)) is in the complement, then ((a,b)\notin R). Step 2: If ((b,a)) were in (R), symmetry would force ((a,b)\in R), a contradiction. Step 3: Therefore ((b,a)) is also in the complement.चरण 1: यदि ((a,b)) पूरक में है, तो ((a,b)) (R) में नहीं है। चरण 2: अगर ((b,a)) (R) में होता, तो सममितता से ((a,b)) भी (R) में होता, जो गलत है। चरण 3: इसलिए ((b,a)) भी पूरक में है।
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