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Is the function (f:\mathbb{Z}\to\mathbb{Z}), where (f(n)=2n+1), onto or not?फलन (f:\mathbb{Z}\to\mathbb{Z}) जहाँ (f(n)=2n+1), आच्छादी है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No because only odd integers are obtainedनहीं क्योंकि केवल विषम पूर्णांक मिलते हैं
Step 1: (2n+1) is always an odd integer. Step 2: The codomain (\mathbb{Z}) also contains even integers, which are not images. Step 3: For integer functions, parity checks are very useful for onto questions.चरण 1: (2n+1) हमेशा विषम पूर्णांक होता है। चरण 2: सहप्रांत (\mathbb{Z}) में सम पूर्णांक भी हैं, जो प्रतिबिंब नहीं बनते। चरण 3: पूर्णांकों पर आच्छादिता में सम-विषम जाँच बहुत उपयोगी है।
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