There are two "universal" gates NOR and NAND. It is said that you can create all the logic gates with any combination of just these two. Logic.ly is a fantastic online tool that lets you play with binary logic gates.
See if you can use Logic.ly to create the NOT, OR, AND, and XOR functions using only NORor only NAND gates.
See if you can use Logic.ly to create any of the gates using a combination of only NOR and AND gates.