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Actually, I think we're headed toward symbolic logic and Boolean Algebra.

That's kind of boring. It's formalized pedagogy and not real mathematics. If she has talent in mathematics, I'd encourage her to pursue it until she's had enough to decide it's not for her.

Here's a problem

Let there be six people in a room. Every pair of them either has met before or has not. Prove that there is either (1) a subset of three of them such that each one has met the other two or (2) a subset of three of them such that each one has not met either of the other two.

Prove that this is not necessarily true for a room with a total of 5 people.

Now the hard one: How many people need to be in the room for the conclusion of the first problem to hold where "three" is replaced by "four"?

Just for fun.

I'll give her the problem and see what she does with it.

The symbolic logic has an insidious goal (along the lines of what Carnap did with philosophical problems): develop a computer program to analyze law for constitutionality. It's a worthy project.