For all p, such that 1 ≤ p ≤ 100, if n(Ap)=p+2 and A1 ⊂ A2 ⊂ A3 ⊂ ⋅s ⊂ A100 and displaystyle⋂p=3100 Ap=A, then n(A)=

Question

For all p, such that 1 ≤ p ≤ 100, if n(Ap)=p+2 and A1 ⊂ A2 ⊂ A3 ⊂ ⋅s ⊂ A100 and displaystyle⋂p=3100 Ap=A, then n(A)= (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

(i) When A1 ⊂ A2 ⊂ ldots ⊂ An then displaystyle⋂i=1n Ai=A1 (ii) If A ⊂ B, then A ∩ B=A. (iii) displaystyle⋂p=3100 Ap=A3. (iv) Find n(A3) by using n(Ap)=p+2.

Q. For all $p$ , such that $1 \leq p \leq 100$ , if $n (A_{p}) = p + 2$ and $A_{1} \subset A_{2} \subset A_{3} \subset \dots \subset A_{100}$ and $p = 3 ⋂ 100 A_{p} = A$ , then $n (A) =$

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(i) When $A_{1} \subset A_{2} \subset \dots \subset A_{n}$ then $i = 1 ⋂ n A_{i} = A_{1}$ (ii) If $A \subset B$ , then $A \cap B = A$ .
(iii) $p = 3 ⋂ 100 A_{p} = A_{3}$ .
(iv) Find $n (A_{3})$ by using $n (A_{p}) = p + 2$ .

Q. For all p, such that 1≤p≤100, if n(Ap​)=p+2 and A1​⊂A2​⊂A3​⊂⋯⊂A100​ and p=3⋂100​Ap​=A, then n(A)=

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(i) When A1​⊂A2​⊂…⊂An​ then i=1⋂n​Ai​=A1​ (ii) If A⊂B, then A∩B=A. (iii) p=3⋂100​Ap​=A3​. (iv) Find n(A3​) by using n(Ap​)=p+2.

Q. For all $p$ , such that $1 \leq p \leq 100$ , if $n (A_{p}) = p + 2$ and $A_{1} \subset A_{2} \subset A_{3} \subset \dots \subset A_{100}$ and $p = 3 ⋂ 100 A_{p} = A$ , then $n (A) =$

(i) When $A_{1} \subset A_{2} \subset \dots \subset A_{n}$ then $i = 1 ⋂ n A_{i} = A_{1}$ (ii) If $A \subset B$ , then $A \cap B = A$ .
(iii) $p = 3 ⋂ 100 A_{p} = A_{3}$ .
(iv) Find $n (A_{3})$ by using $n (A_{p}) = p + 2$ .