Question

For all p, such that `1leple100,n(A_(p))=p+1` and `A_(1)subA_(2)sub. . .. .subA_(100)`. Then `underset(p=1)overset(100)(U)A_(p)` contains. _______elements
A. 99
B. 100
C. 101
D. 102

Answer 1

Correct Answer - C
(i) Recall the definition of union of sets and subsets. (ii) If `AsubB`, then `A cupB=B`.
(iii) `underset(n=1)overset(100)(U)A_(n)=A_(100)`.
(iv) Now evalute `n(A_(100))` by using the given condition.