Computer representation of finite sets
Agree on some ordering a1,a2,…,an of the elements of U.
Represent a subset S of U with the bit string of length n, where
the ith bit is 1 if ai belongs to S and is 0 otherwise.
Example: Let U={1,2,3,4,5,6,7,8}. What bit string represents {4,2,5}?
- What would be the representation of the complement of {4,2,5}?
Answer: 1 0 1 0 0 1 1 1 (the negation of the representation
- What would be the representation of S ? T ?
Answer: the conjunction of the representations of S and T.
- What would be the representation of S ? T ?
Answer: the disjunction of the representations of S and T.