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If (f:{2,4,6}\to{0,1}), where (f(n)=0) when (n) is even and (f(n)=1) when (n) is odd, why is (f) not onto?यदि (f:{2,4,6}\to{0,1}), (f(n)=0) जब (n) सम हो और (f(n)=1) जब (n) विषम हो, तो (f) आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (1) has no preimageक्योंकि (1) का कोई पूर्वप्रतिबिंब नहीं है
Step 1: All domain elements (2,4,6) are even. Step 2: Therefore, the function value is always (0), and (1) is never obtained. Step 3: If even one codomain value is missed, the function is not onto.चरण 1: प्रांत के सभी अवयव (2,4,6) सम हैं। चरण 2: इसलिए फलन का मान हमेशा (0) है और (1) कभी नहीं मिलता। चरण 3: सहप्रांत का कोई एक मान भी छूट जाए तो फलन आच्छादी नहीं होता।
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