# Front-door criteria - what does the second requirement mean?

I'm reading Causal Inference in Statistics: A Primer by Pearl, et. al. and I'm a little confused by the definition of front door. The definition in the book (Definition 3.4.1) is:

A set of variables, Z is said to satisfy the front-door criterion relative to an ordered pair of variables (X, Y) if:

1. Z intercepts all directed paths from X to Y
2. There is no unblocked path from X to Z
3. All backdoor paths from Z to Y are blocked by X.

I understand the first and third requirements. But, the second criteria, I'm a little confused. Here is the situation which confused me. Let's say my causal graph looks like this:

So, let's say I set Z = {B}. This satisfies criteria 1 (since the only path from X to Y goes through B. This also satisfies criteria 3 (since the only back-door path from B to Y is B <-- A <-- X <-- U --> Y and this is blocked by X.

But does it satisfy criteria 2? I think the answer is no because there is an unblocked path from X to Z namely X --> A --> B. As such, my understanding is that I need to make Z = {A, B} to satisfy all three criteria. Or am I missing something and do I need to make Z = {A, B, C}?