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3 cards from this section. Quick, good the night before a test.
What is the cardinality of the union of sets A={1,2,3} and B={2,3,4}?
Count the total unique elements.
Define the term 'cardinality'.
Think about how many different items you have.
What is the principle of inclusion-exclusion primarily used for?
Think about what complication overlaps create when counting.
True or False: The cardinality of |A ∪ B| is equal to |A| + |B| only if there is no overlap.
Consider how overlaps affect counts.
Given sets A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}. Calculate |A ∪ B ∪ C|.
Follow the general formula for three sets carefully.
Using the principle of inclusion-exclusion, prove for n = 4 sets that |A1 ∪ A2 ∪ A3 ∪ A4| can be expanded in terms of their pairwise and higher-order intersections.
Ensure every intersection's contribution is correctly signed and counted.
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