Solve the following problems involving multiplexors. Assume inverted inputs are available.

(a) Implement a 2-to-1 MUX using AND-OR logic. Show the K-Map.

(b) Implement a 2-input AND gate using a 2-to-1 MUX.

(c) Implement a 2-input OR gate using a 2-to-1 MUX.

(d) Implement an inverter using a 2-to-1 MUX.

(e) Implement a 2-input NAND gate using a 2-to-1 MUX.