22.1. Counting Using Principle of Inclusion-Exclusion

Try these first

1. 1.

   What is the formula for the cardinality of the union of two sets?

   Hint

   Think about over-counting!

2. 2.

   If |A| = 5 and |B| = 3, and |A ∩ B| = 2, what's |A ∪ B|?

   Hint

   Use the formula for union!

3. 3.

   How does the principle of inclusion-exclusion help in counting?

   Hint

   Think about adding and subtracting counts.

4. 4.

   The formula for three sets' union primarily adjusts for what?

   • True
   • False

   Hint

   Remember the addition and subtraction scheme!

5. 5.

   In a conference, 100 attendees discussed several topics. If 70 were interested in AI, 50 in Data Science, and 30 in both, determine how many were interested in at least one topic.

   Hint

   Set up each count and adjust using the intersection.

6. 6.

   Consider three libraries A, B, and C with 100, 80, and 60 titles respectively, with overlaps: 30 common in A and B, 20 in A and C, 25 between B and C, and 15 in all three. Find the number of unique titles.

   Hint

   Extract each size and substitute into the inclusion-exclusion formula.