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:

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.