Find the smallest set A such that A 1, 2 = 1, 2, 3, 5, 9 . - Vidyadip

Question

Find the smallest set A such that $\text{A}\cup\{1, 2\} = \{1, 2, 3, 5, 9\}.$

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Answer

The smallest set A such that $\text{A}\cup\{1, 2\} = \{1, 2, 3, 5, 9\}$ is {3, 5, 9}
$\because\{3, 5, 9\}\cup\{1, 2\} = \{1, 2, 3, 5, 9\}$
Any other set B such that $\text{B}\cup\{1, 2\} = \{1, 2, 3, 5, 9\}$ will contain A.For example we contake B to be {1, 3, 5, 9} or {1, 2 3, 5, 9}.
Clearly B contains A = {3, 5, 9}.

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