Question

determine whether \\(subseteq\\), \\(subset\\), both, or neither can be placed in each blank to form a true statement.\\({x|x\\) is someone who is alive or someone who is dead\\}\underline{\quad\quad}\\{x|x\\) is a person\\}\
select the correct answer below.\
\\(\bigcirc\\) \\(\subset\\)\
\\(\bigcirc\\) neither\
\\(\bigcirc\\) \\(\subseteq\\)\
\\(\bigcirc\\) both

Explanation:

Step1: Define the two sets

Let $A = \{x|x \text{ is someone who is alive or someone who is dead}\}$
Let $B = \{x|x \text{ is a person}\}$

Step2: Analyze set equality

Every person is either alive or dead, and every individual in set $A$ is a person. Thus, $A = B$.

Step3: Evaluate subset symbols

• $\subseteq$: A set is always a subset of itself, so $A \subseteq B$ is true.
• $\subset$: This denotes a proper subset (where $A

eq B$). Since $A=B$, $A \subset B$ is false.

Answer:

$\subseteq$