Logic gates in code

You will build logic gates from one gate, the NAND gate, as a factory would.

The idea. A NAND gate gives $0$ only when both inputs are $1$. NOT is a NAND gate with its two inputs tied. AND is a NAND gate followed by a NOT. OR is a NOT on each input followed by a NAND gate.

Your tasks.

1. In nand, return the output of a NAND gate for inputs a and b, each $0$ or $1$.
2. In not_gate, return the NOT of a. Use only nand.
3. In and_gate, return a AND b. Use only nand and not_gate.
4. In or_gate, return a OR b. Use only nand and not_gate.