I think the point of these basic identities, as they're called in the text, is to give guidance for simplifying code in the condition.
Fair enough - and anything that helps is ... helpful!
I find it helpful to read an expression. Actually read it, rather than just letting it hit the eyes as a sequence of symbols. Often I'll mentally respond to myself "Oh!, that just means...". The best rule of thumb, though, is never to write long, ugly, unintelligible conditions. It costs nothing to break them up into component subexpressions and assign them meaningfully named variables.