Universality of switches. Prove that switches and gates are equivalent models for combinational circuits, in the sense that given any network of wires, on/off switches, and input-off switches, you can...

Universality of switches. Prove that switches and gates are equivalent models for combinational circuits, in the sense that given any network of wires, on/off switches, and input-off switches, you can build an interconnected network of gates that computes the same outputs, and vice versa. Hint: This proof amounts to adding AND NOT to the list in the previous question.