let $B$ be the set of all binary strings over the alphabet $\{0,1\}$. Consider the function $f \colon B\to B$ such that for any string $x$, the value $f(x)$ is obtained by replacing all $0$'s in $x$ by $1$'s and all $1$'s in $x$ by $0$'s. Is the function bijective? Can anyone tell me why?
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