Question

For all $p$, such that $1 \leq p \leq 100$, if $n\left(A_p\right)=p+2$ and $A_1 \subset A_2 \subset A_3 \subset \cdots \subset A_{100}$ and $\displaystyle\bigcap_{p=3}^{100} A_p=A$, then $n(A)=$

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

(i) When $A_1 \subset A_2 \subset \ldots \subset A_n$ then $\displaystyle\bigcap_{i=1}^n A_i=A_1$ (ii) If $A \subset B$, then $A \cap B=A$.
(iii) $\displaystyle\bigcap_{p=3}^{100} A_p=A_3$.
(iv) Find $n\left(A_3\right)$ by using $n\left(A_p\right)=p+2$.