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Smallest Set A with A∪{1,2}={1,2,3,5,9} | JEE Sets

JEE Maths question with a full step-by-step solution.

Question
The smallest set AA such that A∪{1,2}={1,2,3,5,9}A \cup \{1, 2\} = \{1, 2, 3, 5, 9\} is:
A{1,3,5,9}\{1, 3, 5, 9\}
B{3,5,9}\{3, 5, 9\}correct
C{3,9}\{3, 9\}
D{2,5,9}\{2, 5, 9\}
Solution
A∪{1,2}={1,2,3,5,9}.A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}.
 The elements 1,21, 2 are supplied by {1,2}\{1, 2\}, so AA need not contain them. The elements 3,5,93, 5, 9 are not in {1,2}\{1, 2\}, so they must come from AA.
∴A={3,5,9}.\therefore A = \{3, 5, 9\}.
 Correct answer: (2)
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