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Question
If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.
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Solution
Given, f : A → B and g : B → C are one - one.
Then, gof : A → B
Let us take two elements x and y from A, such that
(gof) (x) = (gof) (y)
⇒ g (f (x)) = g (f (y))
⇒ f (x) = f (y) (As, g is one-one)
⇒ x = y (As, f is one-one)
Hence, gof is one-one.
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