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Let $$S = \{1, 2, 3, \ldots, 2008\}$$. Find the number of elements in the set $$\{(A, B) \mid A \cup B = S\}$$
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is $$3^{2008}$$, too long to enter as a number. For $$A \cup B = S$$, each element of S must be in A only, in B only, or in both, giving 3 independent choices for each of the 2008 elements. So the number of ordered pairs $$(A, B)$$ is $$3^{2008}$$.
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