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If (A={1,2,3,4}), what is the number of reflexive relations on (A)?यदि (A={1,2,3,4}), तो (A) पर स्वपरक संबंधों की संख्या कितनी होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2^{12})(2^{12})
Step 1: (A\times A) has (4^2=16) pairs. Step 2: Reflexivity makes (4) self-pairs compulsory, leaving (12) pairs free. Step 3: Therefore, the number of reflexive relations is (2^{12}).चरण 1: (A\times A) में (4^2=16) युग्म हैं। चरण 2: स्वपरकता के लिए (4) स्वयं युग्म अनिवार्य हैं, इसलिए (12) युग्म स्वतंत्र हैं। चरण 3: इस कारण स्वपरक संबंधों की संख्या (2^{12}) है।
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