2021 AIME II Problems/Problem 6
Problem
For any finite set 
, let 
denote the number of elements in . FInd the number of ordered pairs 
such that 
and 
are (not necessarily distinct) subsets of 
that satisfy![\[|A| \cdot |B| = |A \cap B| \cdot |A \cup B|\]](http://latex.artofproblemsolving.com/a/8/c/a8c5056f13bbfd71412164ca53b71c92395e5812.png)
Solution
We can't have a solution without a problem.
See also
| 2021 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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