Is {Ø, {Ø, {Ø}}∈ C? where C = {Ø, {Ø},{Ø,{Ø}},{Ø, {Ø},{Ø,{Ø}}}}.Group startsTrue or FalseTrue, unselectedFalse, unselected

To determine whether $\{ \emptyset, \{ \emptyset, \{ \emptyset \} \} \} \in C$, where $C = \{ \emptyset, \{ \emptyset \}, \{ \emptyset, \{ \emptyset \} \}, \{ \emptyset, \{ \emptyset \}, \{ \emptyset, \{ \emptyset \} \} \} \}$, we need to check if the set $\{ \emptyset, \{ \emptyset, \{ \emptyset \} \} \}$ is an element of $C$.

Step 1: Identify the set in question

The set we are examining is $\{ \emptyset, \{ \emptyset, \{ \emptyset \} \} \}$.

Step 2: List the elements of set $C$

The elements of $C$ are:

1. $\emptyset$
2. $\{ \emptyset \}$
3. $\{ \emptyset, \{ \emptyset \} \}$
4. $\{ \emptyset, \{ \emptyset \}, \{ \emptyset, \{ \emptyset \} \} \}$

Step 3: Check for membership

Now we check if $\{ \emptyset, \{ \emptyset, \{ \emptyset \} \} \}$ is one of the elements listed:

• It is not $\emptyset$.
• It is not $\{ \emptyset \}$.
• It is $\{ \emptyset, \{ \emptyset \} \}$ (but the second element is $\{ \emptyset, \{ \emptyset \} \}$).
• It is not $\{ \emptyset, \{ \emptyset \}, \{ \emptyset, \{ \emptyset \} \} \}$.

Conclusion

The set $\{ \emptyset, \{ \emptyset, \{ \emptyset \} \} \}$ matches none of the components in set $C$. Therefore, the answer to the statement "Is $\{ \emptyset, \{ \emptyset, \{ \emptyset \} \} \} \in C$?" is False.

Final Answer

False.