My memory of logic class in college is so clear and it seems so simple, but when I look for sources to teach my kids formal logic (or Boolean algebra), I can't find anything useful. Some books are so caught up in arcane terminology that they are pretty much unreadable. Other books are focused on critical thinking and only include formal logic as one aspect of it. And the largest selection of "logic" books are full of puzzles that are entertaining but have nothing to do with formal logic. The best options I've found are books on Boolean algebra for people interested in learning about computer programming - at least they are readable and coherent.
What I want is a book that explains, clearly and concisely, the ways to think about connections between statements: not, and, or, if/then. I want it to distill what I learned in the college philosophy class plus the logic I learned in math classes, so that I can teach my kids how to think carefully about the statements that they make or encounter. It's about thinking clearly and analytically, not about learning jargon or being able to deconstruct an advertisement. So far, I've found one book on critical thinking that has some chapters I can use, supplemented by a computer science book and my memory of set theory and Venn diagrams (which I love).
The other thing I want to teach them is the most common logical fallacies, or false arguments. I at least have a book that I can use as a guide for this, but it is bible-based so I will have to rework most of it before I give it to my kids. Fallacies are fun to spot in arguments, especially when kids can catch adults in them, and they lead to better thinking. I don't care if my kids remember that "ad hominen" means "against the man", but I do want them to recognize that attacking the person making an argument does not invalidate the argument.
Deconstructing advertising can wait a year or two.