22.1.1. Introduction to the Principle of Inclusion-Exclusion

Try these first

1. 1.

   What is the cardinality of the union of two sets A and B, given |A|=10 and |B|=12 with |A ∩ B|=5?

   Hint

   Use the union formula.

2. 2.

   Define what is meant by 'intersection' in set theory.

   Hint

   Think about shared elements.

3. 3.

   What formula would you use to find the number of elements in |A ∪ B|?

   • |A| + |B|
   • |A| + |B| - |A ∩ B|
   • |A| - |B|

   Hint

   Remember why we subtract the intersection!

4. 4.

   True or False: The principle of inclusion-exclusion can be applied to more than two sets.

   • True
   • False

   Hint

   Think about how we can add more elements.

5. 5.

   You have three sets: A has 5 elements, B has 3 elements, and C has 4. The intersections are |A ∩ B| = 2, |A ∩ C| = 1, |B ∩ C| = 1 and |A ∩ B ∩ C| = 0. Calculate |A ∪ B ∪ C|.

   Hint

   Follow the inclusion-exclusion steps carefully.

6. 6.

   Draw a Venn diagram for two sets A and B with |A|=6, |B|=4, and |A ∩ B|=2. Label the individual regions.

   Hint

   Consider each section of the diagram and how they relate.