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Why is (f:\mathbb{Z}\to\mathbb{Z}), (f(n)=2n+1), not onto?फलन (f:\mathbb{Z}\to\mathbb{Z}), (f(n)=2n+1) सर्वाच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because even integers are not obtainedक्योंकि सम पूर्णांक नहीं मिलते
Step 1: (2n+1) is always an odd integer. Step 2: The codomain (\mathbb{Z}) contains even integers such as (0), (2), and (-2), but they are not images. Step 3: For integer functions, parity is a quick way to test onto property.चरण 1: (2n+1) हमेशा विषम पूर्णांक होता है। चरण 2: सहप्रांत (\mathbb{Z}) में (0), (2), (-2) जैसे सम पूर्णांक भी हैं, पर वे छवि नहीं बनते। चरण 3: पूर्णांक फलनों में सम-विषम प्रकृति से सर्वाच्छादकता जल्दी जाँची जाती है।
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