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If (f:A\to B), (A={1,2,3,4}), (B={a,b,c}), and (f={(1,a),(2,b),(3,b),(4,c)}), what type of function is (f)?यदि (f:A\to B), (A={1,2,3,4}), (B={a,b,c}), और (f={(1,a),(2,b),(3,b),(4,c)}), तो (f) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Onto but not one-oneआच्छादक पर एक-एकी नहीं
Step 1: All three elements (a,b,c) appear as images, so the function is onto. Step 2: Both (2) and (3) map to (b), so it is not one-one. Step 3: While deciding the type, check both the range and repeated images.चरण 1: (a,b,c) तीनों छवि के रूप में मिलते हैं, इसलिए फलन आच्छादक है। चरण 2: (2) और (3) दोनों (b) पर जाते हैं, इसलिए एक-एकी नहीं है। चरण 3: फलन की प्रकृति तय करते समय परास और दोहराई हुई छवियाँ दोनों देखें।
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