I'll start this discussion with a digression. That's something I'm prone to do, so bear with me. This explanation is supposed to be suitable for someone with a minimal background in math or science, perhaps even suitable for a poet. Truth tables are a way of determining, from syntax alone, the truth value of a sentence. So I'll start to unpack what I've babbled above.
Logic is many things to many different people.
There are some interesting conclusions drawn in Computability and Logic that I'm just beginning to appreciate eleven years after I first made my acquaintance with the book. Many children are fascinated by the axiomatic approach to Euclid's geometry in school. . . Oh, I can see you're really underwhelmed. That is to say, whenever you know that A implies B, and you know A to be true, you know B to be true. This is a powerful thing, something not to be scoffed at.