Translating Logic Tables into boolean algebra functions

I have been working through the chapter and have figured out how to translate the boolean algebra functions into working diagrams but I am having trouble making the functions using the logic tables. Can anyone give me any helpful hints or examples?

When you reach more complex gates, you always need to think if you can use gates that you've already built and how to combine them. In the case of multi-bit gates, it helps A LOT to do the things with just one-bit (this is a common practice in, for example, combinatorics), and then extrapolate your results to the remaining bits, because they all do would do the same.