We can use booleans to encode sets. Consider this:

The 1 toggles whether a number is present or not on the set.

Boolean Operations

One nit trick of using the above representation is that to perform union, intersection, and complement we can use boolean operators.

Intersection

110 = {1,2} 010 = {1}

110 & 010 = 010= {1}

Union

110 = {1,2} 101 = {0, 2}

110 | 101 = 111= {0, 1, 2}

Complement

110= {1, 2}

~110 = 001 = {0}