22.2. Example Problems

Try these first

1. 1.

   Using sets A = {1, 2}, B = {2, 3}, calculate |A ∪ B|.

   Hint

   Apply the principle of inclusion-exclusion.

2. 2.

   If |A| = 4 and |B| = 6 with |A ∩ B| = 2, what is |A ∪ B|?

   Hint

   Remember the formula for union of two sets.

3. 3.

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

   • |A ∪ B| = |A| + |B|
   • |A ∪ B| = |A| + |B| - |A ∩ B|
   • |A ∪ B| = |A| - |B|

   Hint

   Remember how elements are counted in both sets.

4. 4.

   True or False: The inclusion-exclusion principle can be applied to any number of sets.

   • True
   • False

   Hint

   Think about expanding the principle beyond two sets.

5. 5.

   You have 10 different books, and you want to choose at least 3 for a reading group. How many selections can you make without duplicating those books?

   Hint

   Consider breaking down the selections by the number of books chosen.

6. 6.

   In a class of 50 students, 20 study Math, 30 study Science, 10 study both. How many study only one subject?

   Hint

   Draw a Venn diagram and look at overlaps.