Set Theory (continued)
union
of two sets A
and B is
the set of items contained in
at least one of the sets; that is, A
È B =
{x |
x Î A
or x Î
B }.
The intersection
of two sets A
and B is
the set of items contained in both sets; that is, A
Ç B
= {x
| x Î
A and x
Î B }.
This intersection is also written AB.
The complement
of a set A
is the set of all
items not contained in the set; that is, A¢
= {x |
x not
in A}.
Distributive Laws. For
any sets A,
B, and
C, (A
È B)
Ç C =
(A Ç
C) È
(B Ç
C) and
(A
Ç B)
È C =
(A È
C) Ç
(B È
C).