1. The problem asks for the complement of set B relative to set A, written as $B \mid A$ or $A \setminus B$, meaning all elements in $A$ that are not in $B$. 2. First, find the elements of set $A$: $A = \{x \in \mathbb{Z} \mid x^{2} \leq 4 \}$ means all integers $x$ whose square is less than or equal to 4. Since $x^{2} \leq 4$ implies $-2 \leq x \leq 2$, the elements of $A$ are: $$A = \{-2, -1, 0, 1, 2\}$$ 3. Next, find the elements of set $B$: $B = \{x \in \mathbb{Z} \mid |x| < 1\}$ means all integers whose absolute value is less than 1. The only integer satisfying $|x| < 1$ is 0, so: $$B = \{0\}$$ 4. Now find $B \mid A$ which equals $A$ without elements in $B$: $$B \mid A = A \setminus B = \{-2, -1, 0, 1, 2\} \setminus \{0\} = \{-2, -1, 1, 2\}$$ 5. Final answer: $$B \mid A = \{-2, -1, 1, 2\}$$