Proof of Cantor-Bernstein-Schröder theorem using the Knaster-Tarski Theorem
Solution 1:
If you define $F(X)=f[X]$, then the fixed-point of $F$ will fail to contain $A-B$ (for example, $\varnothing$ is a fixed-point!). Then $g$ will fail to map the elements of $A-B$ into $B$.