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 $B=\{x | x^c \in A\}$

Is there any characterization for such a set? I have to example for it. But I want to find an IFF condition for such sets...

$e1)$ $A=\{x|$ first coordinate of $x$ is  $1\}$ 

$e2)$ Fix an odd number of coordinates. $A= \{x| x$  contains at least half  of coordinates equal to $1\}$

` [For even number there is a similar example]`

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P.S. Asked It before Here: https://math.stackexchange.com/questions/2135708/when-set-of-complements-is-equal-to-complement-of-set