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If (f:A\to B) and (g:B\to C) are both one-one functions, which statement about (g\circ f) is correct?यदि (f:A\to B) और (g:B\to C) दोनों एकैकी फलन हैं, तो (g\circ f) के बारे में सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (g\circ f) will be one-one(g\circ f) एकैकी होगा
Step 1: Suppose ((g\circ f)(a_1)=(g\circ f)(a_2)). Step 2: Then (g(f(a_1))=g(f(a_2))); since (g) is one-one, (f(a_1)=f(a_2)), and since (f) is one-one, (a_1=a_2). Step 3: The composition of two one-one functions is always one-one.चरण 1: मान लें ((g\circ f)(a_1)=(g\circ f)(a_2))। चरण 2: (g(f(a_1))=g(f(a_2))), और (g) एकैकी है, इसलिए (f(a_1)=f(a_2)); फिर (f) एकैकी होने से (a_1=a_2)। चरण 3: दो एकैकी फलनों का संयोजन हमेशा एकैकी होता है।
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