CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let the universal set U = {1, 2, 3, ..., 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}. How many elements are there in (A ∪ B)′, the complement of A ∪ B?
The complement has 4 elements. A ∪ B contains 2, 3, 4, 6, 8, 9, 10 and 12, which is 8 elements. Removing these from the 12-element universal set leaves 1, 5, 7 and 11.
- A4
- B6
- C5Correct
- D7
Explanation
A ∪ B = {2,3,4,6,8,9,10,12}, which has 8 elements. The complement has 12 − 8 = 4 elements: {1,5,7,11}. Wait, check: 12 − 8 = 4, so the correct count is 4.
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