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If a set has (5) elements, what is the total number of relations on it?यदि किसी समुच्चय में (5) तत्व हैं, तो उस पर कुल संबंधों की संख्या क्या होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^{25})(2^{25})
Step 1: A relation on a set with (n) elements is a subset of (A\times A). Step 2: Here (A\times A) has (5^2=25) pairs. Step 3: Therefore, the total number of relations is (2^{25}).चरण 1: (n) तत्वों वाले समुच्चय पर संबंध (A\times A) का उपसमुच्चय होता है। चरण 2: यहां (A\times A) में (5^2=25) युग्म होंगे। चरण 3: कुल संबंधों की संख्या (2^{25}) होगी।
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