Logic Puzzle Learning Fun

Some of the best fun I've ever had learning a subject was with the books of Raymond Smullyan. He uses puzzles to make learning logic fun. He starts with puzzles about knights that always tell the truth and knaves that always lie and then leads you to puzzles with combinatory logic and even to puzzles that give you an idea of what Godel's incompleteness theorem is all about.

To give you an idea of the fun this can be, one of his books has the title,
What is the Name of This Book?

Here's an example puzzle. There are two rooms, each with one door. The doors are labeled:

1. In this room there is a lady, and in the other room there is a tiger.
2. In one of these rooms there is a lady, and in one of these rooms there is a tiger.

If one sign is true, and the other false, which door should you pick (assuming you want the lady and not the tiger)?

I'll let you ponder that.