CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let U = {1, 2, 3, ..., 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}. How many elements does (A ∪ B)' have, where the complement is taken with respect to U?
The complement of A ∪ B has 4 elements. The union contains 8 elements, namely 2, 3, 4, 6, 8, 9, 10 and 12, so the elements of U outside it are 1, 5, 7 and 11, giving 12 - 8 = 4.
- A4
- B5Correct
- C6
- D7
Explanation
A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12}, which has 8 elements. Complement has 12 - 8 = 4 elements: {1, 5, 7, 11}. Check: 6 + 4 - 2 = 8 for the union, confirming it. The option 6 wrongly counts only the elements of A.
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