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On (A={1,2,3,4}), how many symmetric relations must contain both ((1,2)) and ((3,4))?(A={1,2,3,4}) पर ऐसे सममित संबंधों की संख्या कितनी है जिनमें ((1,2)) और ((3,4)) दोनों अवश्य हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^8)(2^8)
Step 1: For (4) elements, there are (10) independent groups. Step 2: The groups containing ((1,2)) and ((3,4)) are fixed as included. Step 3: The remaining (8) groups are free, so the number is (2^8).चरण 1: (4) अवयवों के लिए कुल स्वतंत्र समूह (10) हैं। चरण 2: ((1,2)) वाला समूह और ((3,4)) वाला समूह लेना तय हो गया। चरण 3: बचे (8) समूह स्वतंत्र हैं, इसलिए संख्या (2^8) है।
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