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If (f:A\to B) is onto and (g:B\to C) is onto, what can be said about (g\circ f:A\to C)?यदि (f:A\to B) आच्छादी है और (g:B\to C) आच्छादी है, तो (g\circ f:A\to C) के बारे में क्या कहा जा सकता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It will be ontoयह आच्छादी होगा
Step 1: Take any element (c) of (C). Step 2: Since (g) is onto, some (b\in B) has (g(b)=c); since (f) is onto, some (a\in A) has (f(a)=b). Step 3: Therefore ((g\circ f)(a)=c), so the composition is onto.चरण 1: (C) का कोई भी अवयव (c) लें। चरण 2: (g) आच्छादी है, इसलिए कोई (b\in B) है जिससे (g(b)=c); और (f) आच्छादी है, इसलिए कोई (a\in A) है जिससे (f(a)=b)। चरण 3: इसलिए ((g\circ f)(a)=c), अतः संयोजन आच्छादी है।
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