Example 1 · level 1
In a CA coaching class, 26 students opted for Accounts revision, 41 for Law revision and 7 for both. How many opted for at least one?
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- n(A ∪ B) = 26 + 41 − 7 = 60.
Answer: 60
CA FOUNDATION: QUANTITATIVE APTITUDE · SETS, RELATIONS AND FUNCTIONS
Sets: union, intersection and Venn counts
n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Neither = Total − n(A ∪ B). Only A = n(A) − n(A ∩ B).
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Worked examples
Example 2 · level 2
Of a group, 39 read The Economic Times, 56 read Business Standard, and 68 read at least one of them. How many read both?
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- n(A ∩ B) = 39 + 56 − 68 = 27.
Answer: 27
Example 3 · level 3
119 employees of Sharma Traders were surveyed: 48 use UPI, 56 use net banking and 24 use both. How many use UPI only?
Show solution
- Only UPI = 48 − 24 = 24.
Answer: 24