Boole's syllogistic is a way of thinking about relationships between things. Imagine you have a bunch of toys, and some are blue and some are red. Boole's syllogistic helps you figure out if certain things are true based on what you know about the toys.
For example, if you have a rule that says "All blue toys are balls," and you also know that you have a red ball, you can use Boole's syllogistic to figure out that the red ball is not blue. This is because if all blue toys are balls, then anything that is not a ball cannot be blue.
Boole's syllogistic helps you make logical conclusions based on rules and facts that you already know. It's like a puzzle that helps you figure out what must be true based on what you already know.