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Show that if `f : A ->B`and `g : B ->C`are one-one, then `gof : A ->C`is also one-one.

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To show that if \( f: A \to B \) and \( g: B \to C \) are one-one functions, then the composition \( g \circ f: A \to C \) is also one-one, we can follow these steps: ### Step 1: Understand the Definitions A function \( f \) is said to be one-one (or injective) if for any two elements \( x_1, x_2 \in A \): \[ f(x_1) = f(x_2) \implies x_1 = x_2 \] Similarly, \( g \) is one-one if: ...
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