Question
Download Solution PDFWhich of the following statements are true about the sets.
A. 0 EØ
B. Ø E {0}
C. Ø E {Ø}
D. {Ø} ∈ {Ø}
E. {Ø} ⊂ {Ø, {Ø}}
Choose the correct answer from the options given below:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 4.
Key Points:
A.
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Explanation: The empty set () contains no elements.
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Conclusion: False, because is not an element of .
B.
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Explanation: The set has only one element: . The empty set is not listed as an element.
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Conclusion: False, because is not in .
C.
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Explanation: The set has one element: the empty set itself.
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Conclusion: True, because is explicitly an element of .
D.
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Explanation: The set contains only , not itself.
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Conclusion: False, because is not an element of itself.
E.
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Explanation:
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has two elements: and .
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The subset is contained within it.
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Conclusion: True, because every element of (which is just ) is also in
Correct Option:
Only C and E are true.
Answer: Option 4 (C and E only).
Key Concepts:
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(Element of): Checks if an item is directly inside a set.
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Example: is true.
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(Subset of): Checks if all elements of one set are in another.
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Example: is true.
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The empty set () is not an element of every set—only when explicitly included (e.g., ).
This aligns perfectly with Option 4.