5. Given the AVL tree shown in Figure 1, insert key 2 and then key 8. After each insertion, please draw the resulting tree once rebalancing has been performed to preserve the AVL property. (10%)

3. (15%) Boolean function \( f(x, y, z, w) = -x \vee (x \wedge y \wedge z \wedge w) \vee (x \wedge y \wedge z \wedge -w) \). First, find the truth table of function \( f \). Second, simplify the expression of \( f \) to minimize the number of AND, OR, NOT operations. Third, draw out the combinatorial circuit corresponding to your simplified expression. Finally, transform and redraw your combinatorial circuit to contain NAND gates only.

5. Given the AVL tree shown in Figure 1, insert key 2 and then key 8. After each insertion, please draw the resulting tree once rebalancing has been performed to preserve the AVL property. (10%)

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