2017 AIME II Problems/Problem 1
Revision as of 11:33, 23 March 2017 by The turtle (talk | contribs) (Created page with "<math>\textbf{Problem 1}</math> Find the number of subsets of <math>\{1, 2, 3, 4, 5, 6, 7, 8\}</math> that are subsets of neither <math>\{1, 2, 3, 4, 5\}</math> nor <math>\{4,...")
Find the number of subsets of
that are subsets of neither
nor
.
The number of subsets of a set with
elements is
. The total number of subsets of
is equal to
. The number of sets that are subsets of at least one of
or
can be found using complimentary counting. There are
subsets of
and
subsets of
. It is easy to make the mistake of assuming there are
sets that are subsets of at least one of
or
, but the
subsets of
are overcounted. There are
sets that are subsets of at least one of
or
, so there are
subsets of
that are subsets of neither
nor
.
.