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Question
If f : A → A, g : A → A are two bijections, then prove that fog is an injection ?
Solution
Injectivity of fog:
Let x and y be two elements of the domain (A), such that
(fog) (x) = (fog) (y)
⇒ f (g(x)) = f (g(y))
⇒ g (x) = g (y) (As, f is one-one)
⇒ x = y (As, g is one-one)
So, fog is an injection.
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