Can we derive all boolean functions using a 2x1 Multiplexer?
Starting from a standard 2x1 mux:







simulate this circuit &ndash; Schematic created using CircuitLab

You can write its output \$O\$ as a function of \$A, B, C\$:
$$
O = A\cdot\overline{C} + B\cdot C
$$

Starting from here, you have a lot of possibilities.
$$
A = 1, B = 0 \implies O = \overline{C}\\
B = 1 \implies O = A\cdot\overline{C} + 1\cdot C = A + C\\
A = 0 \implies O = B\cdot C
$$

So you already have not, or, and. I think you can work the rest from here.