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{\bf \Large \bf CSC240 Winter 2021 Midterm Assessment Question 5}\\
YOUR NAME and STUDENT NUMBER
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(10 marks)
Recall that, for any set $S$, $\#S$ denotes the number of elements in $S$.\\
For any $n \in \nats$, let $[n] = \{i \in \nats\ | 1 \leq i \leq n\}$.
Give a well-ordering proof that, for all $n \in \nats$,
$$\sum_{A\subseteq [n]} \sum_{B\subseteq [n]} \#(A \cup B) = 3n4^{n-1}.$$
Be sure to explicitly define the predicate you are using.\\
You may use the fact that $\#\{A\ |\ A \subseteq [n]\} = 2^n$.
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{\bf Solution}:
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