Membership vs. subset with nested sets: Let A = {1, 2, {3, 4}, 5}. Which statement holds true?

Introduction / Context:
When sets contain other sets as elements, distinguish “∈” (is an element) from “⊂” (is a subset). Here A contains the set {3,4} as a single element.

Given Data / Assumptions:

• A = {1, 2, {3, 4}, 5}
• Elements of A are: 1, 2, {3,4}, 5

Concept / Approach:
{3,4} is literally listed inside A; therefore {3,4} ∈ A is true. For subset claims, each member must appear individually in A, which 3 and 4 do not.

Step-by-Step Solution:
Check {3,4} ⊂ A → requires 3 ∈ A and 4 ∈ A; false.Check {3,4} ∈ A → true by inspection.Check {{3,4}} ⊄ A → actually {{3,4}} ⊂ A since its only element {3,4} is in A; the “not subset” claim is false.Check {1,3,5} ⊂ A → 3 ∉ A (only {3,4} is present), so false.

Verification / Alternative check:
List elements explicitly to avoid confusing elements with members of nested sets.

Why Other Options Are Wrong:
They misuse subset logic where only element membership holds, or they include elements (like 3) not in A.

Common Pitfalls:
Equating “A contains {3,4}” with “A contains 3 and 4” separately—these are not the same claim.

Final Answer:
{3, 4} ∈ A;