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If a set (A) has (4) elements, how many relations are possible on (A)?यदि किसी समुच्चय (A) में (4) तत्व हैं, तो (A) पर कुल संबंधों की संख्या कितनी होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^{16})(2^{16})
Step 1: A relation on (A) is a subset of (A\times A). Step 2: (A\times A) has (4^2=16) pairs. Step 3: The number of subsets is (2^{16}), so that is the answer.चरण 1: (A) पर संबंध (A\times A) का उपसमुच्चय होता है। चरण 2: (A\times A) में (4^2=16) युग्म होंगे। चरण 3: उपसमुच्चयों की संख्या (2^{16}) होगी, इसलिए यही उत्तर है।
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