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?
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A{3, 4} ⊂ A
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B{3, 4} ∈ A
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C1 ⊂ A
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D{1, 2, 5} ∈ A
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E{{3, 4}} ⊂ A
Answer
Correct Answer: {3, 4} ∈ A
Explanation
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