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Let \(A=\{1,2,3\}\), \(B=\{a,b,c\}\), and \(R=\{(1,a),(2,b),(3,a)\}\). What is the correct classification of \(R\) from \(A\) to \(B\)?मान लें कि \(A=\{1,2,3\}\), \(B=\{a,b,c\}\) तथा \(R=\{(1,a),(2,b),(3,a)\}\) है। \(A\) से \(B\) तक \(R\) का सही वर्गीकरण क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Many-one functionबहु-एक फलन
Every element of \(A\) has exactly one image, so \(R\) is a function. Since both 1 and 3 map to \(a\), it is many-one. Element \(c\) has no preimage, so it is not onto. Exam tip: first check that each input has exactly one output.\(A\) के प्रत्येक अवयव की ठीक एक छवि है, इसलिए \(R\) फलन है। 1 और 3 दोनों की छवि \(a\) है, अतः यह बहु-एक फलन है। \(c\) की कोई पूर्व-छवि नहीं है, इसलिए यह सर्वेक्षी नहीं है। परीक्षा टिप: पहले प्रत्येक input की छवि जाँचें।
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