Example 1 · level 1
If n(A) = 37, n(B) = 40 and n(A ∩ B) = 21, find n(A ∪ B).
Show solution
- n(A ∪ B) = 37 + 40 − 21 = 56.
Answer: 56
CLASS 11 MATHS · SETS
Counting with sets and Venn diagrams
n(A ∪ B) = n(A) + n(B) − n(A ∩ B). For three sets add the singles, subtract the pairs and add back the triple overlap.
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Worked examples
Example 2 · level 2
In a class, 61 students play cricket, 47 play kabaddi and 73 play at least one of the two. How many play both?
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- n(A ∩ B) = 61 + 47 − 73 = 35.
Answer: 35
Example 3 · level 3
In a colony in Patna, families read Hindi (H), English (E) and Marathi (M) newspapers. n(H) = 34, n(E) = 45, n(M) = 50, n(H ∩ E) = 10, n(E ∩ M) = 18, n(H ∩ M) = 17 and n(H ∩ E ∩ M) = 7. How many families read at least one of these papers?
Show solution
- Sum of singles = 129.
- Sum of pairs = 10 + 18 + 17 = 45.
- n(H ∪ E ∪ M) = 129 − 45 + 7 = 91.
Answer: 91