CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
If a set A has 5 elements, how many subsets of A are proper subsets that are also non-empty?
The answer is 30. A five-element set has 2^5 = 32 subsets. Removing the set itself (not proper) and the empty set (not non-empty) leaves 32 − 2 = 30 subsets that are proper and non-empty.
- A30Correct
- B31
- C32
- D29
Explanation
Total subsets = 2^5 = 32. A proper subset excludes A itself, giving 31. Excluding the empty set also gives 30. The figure 31 only removes A itself, but forgets to remove the empty set.
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