22.1.3. Generalization to n Sets

Try these first

1. 1.

   What is the cardinality of the union of sets A = {1, 2} and B = {2, 3}?

   Hint

   Consider what elements are shared.

2. 2.

   How does adding the intersection help when calculating union?

   Hint

   Think about how many times each element appears.

3. 3.

   What does the principle of inclusion-exclusion help prevent?

   • A) Over-counting elements
   • B) Under-counting elements
   • C) Both A and B

   Hint

   Think about how the overlap is handled.

4. 4.

   In how many ways can the intersection of n sets be expressed?

   Hint

   Remember the pattern with positive and negative signs.

5. 5.

   Given sets A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8}, calculate |A ∪ B ∪ C|.

   Hint

   Use inclusion-exclusion carefully for intersections.

6. 6.

   If A1 to A5 have 3, 4, 5, 6, and 7 elements respectively, what is |A1 ∪ A2 ∪ A3 ∪ A4 ∪ A5| if some intersections are known?

   Hint

   Each intersection adjusts the counting!