22.2.3. Generalization for m and n Elements

Try these first

1. 1.

   Calculate |A ∪ B| if |A|=5, |B|=3, and |A ∩ B|=1.

   Hint

   Use the formula for two sets.

2. 2.

   What is the cardinality of the union of two disjoint sets |A|=4 and |B|=5?

   Hint

   If sets are disjoint, there’s no intersection to subtract.

3. 3.

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

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

   Hint

   Review the principle of inclusion-exclusion.

4. 4.

   True or False: Inclusion-Exclusion can only be applied to two sets.

   • True
   • False

   Hint

   Think about how we extended the concept from two to three sets.

5. 5.

   Four students register for three different classes, with some taking multiple classes. How many unique student registrations can be calculated using the principle?

   Hint

   List out overlaps carefully.

6. 6.

   You have 5 distinct colors; how can you calculate the distinct patterns you can create using the inclusion-exclusion principle if some colors must overlap?

   Hint

   Map your color set accurately to find overlaps.