Which 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:

  1. A, B, C, D and E
  2. A, B, C and E only
  3. A, C only
  4. C and E only

Answer (Detailed Solution Below)

Option 4 : C and E only

Detailed Solution

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The correct answer is option 4.

Key Points:

A. 0

  • Explanation: The empty set ( ) contains no elements.

  • Conclusion: False, because 0  is not an element of  .


B. {0}

  • Explanation: The set {0}  has only one element: 0 . The empty set is not listed as an element.

  • Conclusion: False, because   is not in {0} .


C. {}

  • Explanation: The set {}  has one element: the empty set itself.

  • Conclusion: True, because   is explicitly an element of {} .


D. {}{}

  • Explanation: The set {}  contains only  , not {}  itself.

  • Conclusion: False, because {}  is not an element of itself.


E. {}{,{}}

  • Explanation:

    • {,{}}  has two elements:   and {} .

    • The subset {}  is contained within it.

  • 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:

  1.  (Element of): Checks if an item is directly inside a set.

    • Example: {}  is true.

  2.  (Subset of): Checks if all elements of one set are in another.

    • Example: {}{,{}}  is true.

  3. The empty set ( ) is not an element of every set—only when explicitly included (e.g., {} ).

This aligns perfectly with Option 4.

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