o n( A ∪ B ∪ C) = n( A) + n( B) + n( C) – n( A ∩ B) – n( B ∩ C) – n( A ∩ C) + n( A ∩ B ∩ C)
Refer ExamFear Video Lessons for explanation.
Numerical: In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics?
Solution: Let P denote Physics teachers & M denote Maths Teacher. n( M) = 12 n( M ∪ P) = 20 n( M ∩ P) = 4 Applying formula n( M ∪ P) = n( M) + n( P) – n( M ∩ P) Or 20 = 12 + n( P) – 4 Or n( P) = 12 We can also solve this with Venn diagram