Find the Smallest Set A Such That A ∪ {1, 2} = {1, 2, 3, 5, 9}

Solution

We know that:

\[ A \cup \{1,2\} = \{1,2,3,5,9\} \]

The set \( \{1,2\} \) already contains the elements 1 and 2.

Therefore, the remaining elements required in set \( A \) are:

\[ 3,\ 5,\ 9 \]

Hence, the smallest set \( A \) is:

\[ A = \{3,5,9\} \]