1. **State the problem:** We want to find the set $W = \{x \in \mathbb{N} \mid 2x \leq 4 \wedge x > 1\}$. 2. **Understand the conditions:** The set $W$ contains natural numbers $x$ such that both $2x \leq 4$ and $x > 1$ hold true. 3. **Solve the inequality $2x \leq 4$:** $$ 2x \leq 4 $$ Divide both sides by 2: $$ \cancel{2}x \leq \frac{4}{\cancel{2}} \\ x \leq 2 $$ 4. **Combine with the second condition $x > 1$:** We need $x$ such that: $$ 1 < x \leq 2 $$ 5. **Find natural numbers satisfying both:** Natural numbers are $1, 2, 3, \ldots$ Only $x=2$ satisfies $1 < x \leq 2$. 6. **Final answer:** $$ W = \{2\} $$