Black or white – In dire need of grayscale implementation

Today, I had an instruction of a course that, from my point of view is not nearly as formal as it claims to be. It covers several languages for describing and analyzing model behavior, such as LTL, CTL, CTL* and mu-calculus. A lot of handwaving is included and for several weeks now I’ve gotten frustrated with the commonly used word intuition. "You need to use your intuition to solve this." Listen people, I want a proper definition and a couple of months of practice before intuition comes into play.

Intuition is nothing divine or easily learned, it’s the ability to recognize certain situations from previous experience and act as one would in a similar situation. Practice and experience is the key, it doesn’t become common sense until you’ve had a lot of practice. So, please, just give me some proper definitions and a few examples… I guess teachers tend to forget that what seems so simple and self-evident to them, isn’t when you’re just getting acquainted with said formalisms…

I’ve been having some troubles with another course, that requires me to formulate exact proofs and derivations and no handwaving what-so-ever is allowed, but frankly, I’d rather do a subject that is clear on what you need to do and difficult to master, than the opposite. Now, let’s just hope I can pass them both without intuition but with a huge amount of hard work, I need the credits..