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Homework Statement
Let f: X \rightarrow Y be a function. Suppose A is a subset of X. Show that if f is injective, then f(A^{c})\subseteq f(A)^{c}.
Homework Equations
The Attempt at a Solution
If x \in A^{c}, then there is a y \in f(A^{c}) such that f(x)=y. As f is an injection, y \notin f(A), hence y \in f(A)^{c}.
Is that alright?