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If (S={1,2,3,4}) and (A=\mathcal{P}(S)), how many reflexive relations are possible on (A)?यदि (S={1,2,3,4}) और (A=\mathcal{P}(S)) है, तो (A) पर प्रतिवर्ती संबंधों की संख्या कितनी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^{240})(2^{240})
Step 1: (A=\mathcal{P}(S)) has (2^4=16) elements. Step 2: The number of reflexive relations on (A) is (2^{16^2-16}). Step 3: Since (16^2-16=240), the answer is (2^{240}).चरण 1: (A=\mathcal{P}(S)) में (2^4=16) तत्व हैं। चरण 2: (A) पर प्रतिवर्ती संबंधों की संख्या (2^{16^2-16}) होगी। चरण 3: (16^2-16=256-16=240), इसलिए उत्तर (2^{240}) है।
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