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If (A) has (4) elements, what is the number of total relations on (A)?यदि (A) में (4) अवयव हैं तो (A) पर कुल संबंधों की संख्या क्या होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^{16})(2^{16})
Step 1: (A\times A) has (4^2=16) pairs. Step 2: Each subset forms a relation so the total number of relations is (2^{16}). Step 3: For total relations on (n) elements use (2^{n^2}).चरण 1: (A\times A) में (4^2=16) युग्म होंगे। चरण 2: प्रत्येक उपसमुच्चय एक संबंध बनाता है इसलिए कुल संबंध (2^{16}) होंगे। चरण 3: (n) अवयवों पर कुल संबंधों के लिए (2^{n^2}) लगाएँ।
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