Discussion
The power set of \(A \cup B\), where A = {2, 3, 5, 7} and B = {2, 5, 8, 9} is
Answer: B
The union \(A \cup B\) of A = {2, 3, 5, 7} and B = {2, 5, 8, 9} is {2, 3, 5, 7, 8, 9}, which has 6 elements, since 2 and 5 are common to both sets. The power set of a set with n elements has \(2^n\) elements, so
\[ 2^6 = 64 \]The number 256 is \(2^8\), the power set size for 8 elements, which is the count one gets by adding the sizes of the sets without removing the common elements, and 16 is \(2^4\). The keyed answer is 64.
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