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On (A={1,2,3,4}), (R={(a,b):ab\text{ is even}}). Which statement is correct about (R)?समुच्चय (A={1,2,3,4}) पर (R={(a,b):ab\text{ सम है}}) है। (R) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (R) is symmetric(R) सममित है
Step 1: (ab) and (ba) are equal. Step 2: If (ab) is even, then (ba) is also even, so the reverse pair also belongs to the relation. Step 3: Multiplication is commutative, so product-based conditions often preserve symmetry.चरण 1: (ab) और (ba) बराबर होते हैं। चरण 2: यदि (ab) सम है, तो (ba) भी सम होगा, इसलिए उल्टा युग्म भी संबंध में होगा। चरण 3: गुणन में क्रम बदलने से गुणनफल नहीं बदलता।
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