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In the divisibility relation on (A={1,2,3,6}), how many elements can a longest chain contain?समुच्चय (A={1,2,3,6}) पर विभाज्यता संबंध में अधिकतम श्रृंखला में कितने अवयव होंगे?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (3)(3)
Step 1: In a chain, every two elements must be comparable. Step 2: (1\mid2\mid6) and (1\mid3\mid6) are chains of three elements. Step 3: Since (2) and (3) are not comparable, a four-element chain is impossible.चरण 1: एक श्रृंखला में हर दो अवयव तुलनीय होने चाहिए। चरण 2: (1\mid2\mid6) और (1\mid3\mid6) तीन-तीन अवयवों की श्रृंखलाएं हैं। चरण 3: (2) और (3) तुलनीय नहीं हैं, इसलिए चार अवयवों की श्रृंखला नहीं बन सकती।
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