CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
For sets A and B, n(A) = 30, n(B) = 25 and n(A ∪ B) = 45. What is n(A Δ B), the number of elements belonging to exactly one of A or B?
35 elements belong to exactly one of the two sets. The intersection is 30 + 25 - 45 = 10, and removing these from the union of 45 leaves 35, which equals 20 only in A plus 15 only in B.
- A35Correct
- B40
- C45
- D50
Explanation
n(A ∩ B) = 30 + 25 - 45 = 10. Elements in exactly one set = n(A ∪ B) - n(A ∩ B) = 45 - 10 = 35. Check: only A = 20 and only B = 15, total 35. The option 45 mistakenly gives the whole union.
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