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If (f:A\to B) and (g:B\to C) are both one-one, what is (g\circ f)?यदि (f:A\to B) और (g:B\to C) दोनों एकैकी हों तो (g\circ f) कैसा होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Always one-oneहमेशा एकैकी
Step 1: If ((g\circ f)(a_1)=(g\circ f)(a_2)), then (g(f(a_1))=g(f(a_2))). Step 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 one-one.चरण 1: यदि ((g\circ f)(a_1)=(g\circ f)(a_2)) हो तो (g(f(a_1))=g(f(a_2)))। चरण 2: (g) एकैकी है इसलिए (f(a_1)=f(a_2)), और (f) एकैकी है इसलिए (a_1=a_2)। चरण 3: दो एकैकी फलनों का समिश्र भी एकैकी होता है।
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