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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2

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The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?
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A = {2,3,5,7} and B = {2,5,8,9} so, AUB = {2,3,5,7,8,9}
We know, |P(A)| = Number of Subsets of A = 2^|A| 

Therefore, |P(AUB)| = 2^|AUB| => 2^6 => 64

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\( A = \{2, 3, 5, 7\} \) and

\( B = \{2, 5, 8, 9\} \)

The union of \( A \) and \( B \) is \( A \cup B = \{2, 3, 5, 7, 8, 9\} \).

Now, the cardinality of a power set is \( 2^n \), where \( n \) is the number of elements in the original set.

Since \( A \cup B \) has \( 6 \) elements, the cardinality of its power set is \( 2^6 = 64 \).
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