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The Number of Sets of Sets

Source: 1993 National High School Mathematics League, Exam One, Problem 3

February 27, 2020

Problem Statement

Sets A,BA,B satisfy that A∪B={a1,a2,a3}A\cup B=\{a_1,a_2,a_3\}. If A≠BA\neq B, then (A,B)(A,B) is different from (B,A)(B,A). The number of such sets (A,B)(A,B) is (A)8(B)9(C)26(D)27\text{(A)}8\qquad\text{(B)}9\qquad\text{(C)}26\qquad\text{(D)}27
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