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If (A={1,2}), how many total relations can be formed on (A)?यदि (A={1,2}) हो तो (A) पर कुल कितने संबंध बनाए जा सकते हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (16)(16)
Step 1: A relation on (A) is a subset of (A\times A). Step 2: (A\times A) has (2^2=4) pairs so the number of subsets is (2^4=16). Step 3: Remember (2^{n^2}) for total relations on a set with (n) elements.चरण 1: (A) पर संबंध (A\times A) का उपसमुच्चय होता है। चरण 2: (A\times A) में (2^2=4) युग्म हैं इसलिए उपसमुच्चय (2^4=16) होंगे। चरण 3: कुल संबंधों के लिए (2^{n^2}) याद रखें।
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