Problem #1006 - Math All Star

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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 $A$ .

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Let the element in $A$ be $x$ , then by the inclusion-exclusion principle we have $x+x-1001=2007\implies x=\boxed{1504}$

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