Consider $A \subset \{0,1\}^n$ I want $A$ to have $2$ properties. $1.$ $A$ is increasing, i.e., If $x \in A$ and $x \subseteq y$ then $y \in A$ too. [$x \subseteq y$ means that every coordinate of $y$ is greater that or equal to corresponding coordinate of $x$] $2.$ $A^c$ is equal to set...