InclusionExclusion AMC8 Basic
2007
Problem - 1006
Sets $A$ and $B$, shown in the Venn diagram, have the same number of elements. Their union has $2007$ elements and their intersection has $1001$ elements. Find the number of elements in $A$.
Let the element in $A$ be $x$, then by the inclusion-exclusion principle we have $$x+x-1001=2007\implies x=\boxed{1504}$$