Generated set A = {(n−1)/(n+1) : n ∈ W, n ≤ 10} — identify a true statement (Recovery-First): Consider A defined by x = (n−1)/(n+1) for whole numbers n with n ≤ 10. Which statement is correct?

Introduction / Context:The stem uses “0” where standard notation would use ϕ (empty set). Applying Recovery-First, interpret “0 ⊂ A” as “ϕ ⊂ A”. We analyze membership values of A and the truth of each statement under that repair.

Given Data / Assumptions:

• A = { (n−1)/(n+1) : n ∈ W, n ≤ 10 }, with W = {0,1,2,...}
• We compute sample values: n=0 → −1; n=1 → 0; n=2 → 1/3; n=3 → 1/2; ...

Concept / Approach:Check each option against A’s generated values, and fix the nonstandard symbol “0” to ϕ when it denotes the empty set in subset relations.

Step-by-Step Solution:n=1 gives 0, so 0 ∈ A is true as a number, but the stem’s choices mix numeric 0 with set symbols; interpret carefully.1/3 ∈ A since (2−1)/(2+1) = 1/3 → so “1/3 ∉ A” is false.ϕ ⊂ A is always true for any set A (empty set is a subset of every set).

Verification / Alternative check:A contains many fractions in (−1, 1). Regardless of exact contents, ϕ ⊂ A remains universally true; thus the corrected reading of option “0 ⊂ A” becomes the valid statement.

Why Other Options Are Wrong:“0 ⊃ A” is ill-formed; “1/3 ∉ A” is false; “A = ϕ” is false since A is nonempty; “0 ∈ A” mixes numeral vs. set-symbol usage and is ambiguous in the given list.

Common Pitfalls:Confusing numeral 0 with the empty set ϕ; always distinguish element membership from subset relations.

Final Answer:0 ⊂ A