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On (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}). Which statement about (R) is correct?समुच्चय (A={1,2,3,4}) पर (R={(a,b):a+b\text{ सम है}}) है। (R) के बारे में सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is symmetricयह सममित है
Step 1: If (a+b) is even, then (b+a) is also even because changing the order does not change the sum. Step 2: So ((a,b)) being in the relation implies ((b,a)) is also in it. Step 3: Conditions based on commutative operations like addition or multiplication often give symmetry.चरण 1: यदि (a+b) सम है, तो (b+a) भी सम होगा क्योंकि जोड़ का क्रम बदलने से योग नहीं बदलता। चरण 2: इसलिए ((a,b)) होने पर ((b,a)) भी संबंध में होगा। चरण 3: जोड़ या गुणा जैसे अदला-बदली वाले नियम अक्सर सममितता देते हैं।
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