Question

determine whether \\(\subseteq\\), \\(\subset\\), both, or neither can be placed in the blank to make the statement true.\\(a = \\{x \mid x\in\mathbb{n}\text{ and } 2 < x < 5\\}\\)\\(b = \text{the set of all natural numbers between 2 and 5}\\)\\(a\underline{quadquad}b\\)choose the correct answer below.\\(\bigcirc\\) only \\(\subset\\)\\(\bigcirc\\) only \\(\subseteq\\)\\(\bigcirc\\) both \\(\subseteq\\) & \\(\subset\\)\\(\bigcirc\\) none of the above

Explanation:

Step1: List elements of set A

Natural numbers $\mathbb{N}$ are positive integers. For $A = \{x \mid x\in\mathbb{N} \text{ and } 2

Step2: List elements of set B

B is natural numbers between 2 and 5, which are $3,4$. So $B=\{3,4\}$.

Step3: Analyze set relations

• $\subseteq$: A set is a subset of itself, so $A\subseteq B$ is true.
• $\subset$: This denotes a proper subset (A≠B), but $A=B$, so $A\subset B$ is false.

Answer:

only $\subseteq$