Question

determine whether \\(\subseteq\\), \\(\subset\\), both, or neither can be placed in the blank to make the statement true.\\(\\{3, 5, 7, 9, 11\\}\\) ___ \\(\\{11, 5, 7, 9, 3\\}\\)\
choose the correct answer below.\
\\(\circ\\) only \\(\subset\\)\
\\(\circ\\) only \\(\subseteq\\)\
\\(\circ\\) both \\(\subseteq\\) & \\(\subset\\)\
\\(\circ\\) none of the above

Explanation:

Step1: Recall subset definitions

A set $A \subseteq B$ if every element of $A$ is in $B$. A set $A \subset B$ if $A \subseteq B$ and $A
eq B$.

Step2: Compare the two sets

Let $A = \{3, 5, 7, 9, 11\}$ and $B = \{11, 5, 7, 9, 3\}$. All elements of $A$ are in $B$, and $A$ has exactly the same elements as $B$ (set order does not matter), so $A = B$.

Step3: Evaluate symbols

Since $A = B$, $A \subseteq B$ is true (all sets are subsets of themselves). However, $A \subset B$ is false because $A$ is not a proper subset (they are equal).

Answer:

only $\subseteq$