CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
For two sets A and B, n(A) = 40, n(B) = 30 and n(A ∩ B) = 12. What is n(A Δ B), the number of elements belonging to exactly one of the two sets?
The answer is 46. Elements only in A number 40 minus 12, which is 28, and elements only in B number 30 minus 12, which is 18. Adding them gives 46. The union, 58, wrongly includes the 12 common elements.
- A58
- B46Correct
- C34
- D70
Explanation
Only A = 40 − 12 = 28; only B = 30 − 12 = 18. Exactly one set = 28 + 18 = 46. The option 58 is n(A ∪ B) = 40 + 30 − 12, which includes the overlap and so is wrong here.
Did you get it right without looking?
One question tells you little. A timed set on Sets, Relations and Functions, Limits and Continuity shows your real accuracy, how long you take and where you lose marks.
More Sets, Relations and Functions, Limits and Continuity questions
- The function f(x) = (x + 1)/(x² − 9) is not continuous at which real values of x?
- A function f is defined on the real numbers by f(x) = x² − 4x + 7. What is the range of f?
- Which of the following is the set-builder form of the set A = {1, 4, 9, 16, 25}?
- Let f(x) = (x² − 4)/(x − 2) for x ≠ 2, and f(2) = 5. Which statement about f at x = 2 is correct?
- A relation R from set A = {1, 2, 3, 4} to set B = {1, 2, 3, 4, 5, 6} is defined by R = {(x, y) : y = x + 2}. What is the range of R?
- 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?