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On (A={1,2,3,4,5,6}), how many pairs are in (R={(a,b):a-b) is divisible by (3)(})?समुच्चय (A={1,2,3,4,5,6}) पर (R={(a,b):a-b) संख्या (3) से विभाज्य है(}) में कुल कितने युग्म हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (12)(12)
Step 1: Each of the three remainder classes modulo (3) has two elements. Step 2: Only ordered pairs with the same remainder belong to the relation. Step 3: The total number is (2^2+2^2+2^2=12).चरण 1: (3) से भाग देने पर तीनों शेष वर्गों में दो-दो अवयव हैं। चरण 2: समान शेष वाले क्रमित युग्म ही संबंध में आएंगे। चरण 3: कुल संख्या (2^2+2^2+2^2=12) होगी।
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