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Find the number of unordered pairs

Source: Indian RMO 1997 PROBLEM 6

October 26, 2005
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Problem Statement

Find the number of unordered pairs {A,B}\{ A,B \} of subsets of an n-element set XX that satisfies the following: (a) A≠BA \not= B (b) A∪B=XA \cup B = X
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