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Question
Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one
Solution
Let a, b ∈ A such that
(g ° f)(a) = (g ° f)(b)
∴ g[f(a)] = g[f(b)]
∴ f(a) = f(b) ...[∵ g is one-one]
∴ a = b ...[∵ f is one-one]
∴ (g ° f)(a) = (g ° f)(b) ⇒ a = b
∴ g ° f is one-one.
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