Identify the true statement for a set containing a set element: Let A = {1, 2, {3, 4}, 5}. Which one of the following is true?

Introduction / Context:
This is a focused check on membership vs. subset when a set contains another set as an element. We confirm which relation actually holds for A.

Given Data / Assumptions:

• A = {1, 2, {3, 4}, 5}

Concept / Approach:
{3,4} is literally an element of A; thus {3,4} ∈ A is true. A subset claim {3,4} ⊂ A would require 3 and 4 to be elements of A individually, which is not the case.

Step-by-Step Solution:
Check {3,4} ∈ A → true (listed element){3,4} ⊂ A → false (3 ∉ A, 4 ∉ A)1 ⊂ A → false (1 is an element, not a set of elements){1,2,5} ∈ A → false (A does not contain that set)

Verification / Alternative check:
Enumerate elements of A to compare directly against each option.

Why Other Options Are Wrong:
They confuse element membership with subset relations or propose a set A does not contain.

Common Pitfalls:
Writing 1 ⊂ A when only set-valued objects can be subsets.

Final Answer:
{3, 4} ∈ A