2017 AIME II Problems/Problem 1
Problem
Find the number of subsets of that are subsets of neither
nor
.
Solution
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
.
.
See Also
2017 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 0 |
Followed by Problem 2 | |
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