Question

determine whether \\(subseteq\\), \\(subset\\), both, or neither can be placed in the blank to make the statement true.\\({1, 3, 5, 7, 9}\\) ___ \\({5, 9, 3, 7, 1}\\)\
choose the correct answer below.\
\\(\bigcirc\\) only \\(subset\\)\
\\(\bigcirc\\) only \\(subseteq\\)\
\\(\bigcirc\\) both \\(subseteq\\) & \\(subset\\)\
\\(\bigcirc\\) none of the above

Explanation:

Step1: Define subset symbol

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

Step2: Check $\subseteq$ validity

All elements of $\{1, 3, 5, 7, 9\}$ are in $\{5, 9, 3, 7, 1\}$, so $\{1, 3, 5, 7, 9\} \subseteq \{5, 9, 3, 7, 1\}$ is true.

Step3: Define proper subset symbol

A set $A \subset B$ if $A \subseteq B$ and $A
eq B$.

Step4: Check $\subset$ validity

The two sets have identical elements, so $\{1, 3, 5, 7, 9\} = \{5, 9, 3, 7, 1\}$, meaning $\subset$ is false.

Answer:

only $\subseteq$