Use $ \subseteq, \nsubseteq, \subset $, or both $ \subset $ and $ \subseteq$ to make a true statement. -$\{ x \mid x \in N$ and $x 8 \} ........ \{ x \mid x \in N$ and $3

Question

Use $ \subseteq, \nsubseteq, \subset $, or both $ \subset $ and $ \subseteq$ to make a true statement.
-$\{ x \mid x \in N$ and $x > 8 \} ........ \{ x \mid x \in N$ and $3 < x \leq 8 \}$
A) $\subseteq$ and $\subset$
B) $\subseteq$
C) $\subset$
D) $\nsubseteq$

Quizplus · Accepted Answer

The set $\{ x \mid x \in N$ and $x > 8 \}$ consists of natural numbers greater than 8, while the set $\{ x \mid x \in N$ and $3 < x \leq 8 \}$ consists of natural numbers greater than 3 but less than or equal to 8. There is no overlap between these two sets; therefore, the first set is not a subset of the second set, making the correct symbol $\nsubseteq$.

Use ⊆,⊈,⊂ \subseteq, \nsubseteq, \subset ⊆,⊈,⊂ , or Both ⊂ \subset ⊂

Use $\subseteq, \nsubseteq, \subset$ , or Both $\subset$