1. The problem asks us to determine why the set $A = \{-1, 0, 1\}$ is not a subset of the set $B = \{1, -1, 2, -2\}$. 2. Recall the definition: A set $A$ is a subset of $B$ (written $A \subseteq B$) if every element of $A$ is also an element of $B$. 3. Let's check each element of $A$ to see if it belongs to $B$: - $-1 \in B$ because $-1$ is in $B$. - $0 \notin B$ because $0$ is not in $B$. - $1 \in B$ because $1$ is in $B$. 4. Since $0 \notin B$, not all elements of $A$ are in $B$. Therefore, $A \not\subseteq B$. 5. Filling in the blanks: $0 \in A$ but $0 \notin B$. Final answer: $A \not\subseteq B$ since $0 \in A$ but $0 \notin B$.