CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let A = {x : x is a natural number, 1 ≤ x ≤ 20 and x is a multiple of 3} and B = {x : x is a natural number, 1 ≤ x ≤ 20 and x is a multiple of 4}. The number of proper subsets of A ∪ B is:
A has six elements and B has five, and only 12 is common, so A ∪ B has 10 elements. The number of proper subsets is 2^10 − 1 = 1023.
- A255
- B511Correct
- C127
- D1023
Explanation
A = {3,6,9,12,15,18} has 6 elements; B = {4,8,12,16,20} has 5. Common element: 12 only (multiple of 12 up to 20). So |A∪B| = 6+5−1 = 10. Proper subsets = 2^10 − 1 = 1023. Check the options: 1023 is the key; 511 is 2^9−1 which arises from wrongly using 9 elements.
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