How many numbers between 1 and 100 (inclusive) are divisible by 3 or 4?

Use the inclusion-exclusion principle to solve this problem.

|A or B| = |A| + |B| - |A and B|

 

Let set A = the 3s in [1...100] and set B = the 4s in [1...100]

|A| = 100 / 3 = 33

|B| = 100 / 4 = 25

|A and B| = 100 / (A*B) = 100 / 12 = 8

Therefore |A or B| = 33 + 25 - 8 = 50

The answer is 50.

 

 

(In this problem, || isn't the absolute value. It means the cardinality of the sets A and B.)