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If (|A|=5) and (|B|=3), how many onto functions are there from (A) to (B)?यदि (|A|=5) और (|B|=3), तो (A) से (B) पर आच्छादक फलनों की संख्या कितनी होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (150)(150)
Step 1: Total functions are (3^5). Step 2: By inclusion-exclusion, onto functions (=3^5-\binom{3}{1}2^5+\binom{3}{2}1^5=243-96+3=150). Step 3: For counting onto functions on finite sets, use inclusion-exclusion.चरण 1: कुल फलन (3^5) हैं। चरण 2: समावेशन-अपवर्जन से आच्छादक फलन (3^5-\binom{3}{1}2^5+\binom{3}{2}1^5=243-96+3=150)। चरण 3: परिमित समुच्चयों में onto count के लिए inclusion-exclusion याद रखें।
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