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If (A={1,2,3,4,5}), the number of symmetric relations on (A) equals which of the following?यदि (A={1,2,3,4,5}) है, तो (A) पर सममित संबंधों की संख्या किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^{15})(2^{15})
Step 1: The number of symmetric relations is (2^{\frac{n(n+1)}{2}}). Step 2: Here (n=5), so the count is (2^{\frac{5(6)}{2}}=2^{15}). Step 3: For larger sets, use the same rule and substitute (n) carefully.चरण 1: सममित संबंधों की संख्या (2^{\frac{n(n+1)}{2}}) होती है। चरण 2: यहाँ (n=5), इसलिए (2^{\frac{5(6)}{2}}=2^{15}) मिलेगा। चरण 3: बड़े समुच्चय में भी वही नियम लगाएँ, केवल (n) सही रखें।
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