I have two small questions:

1 - In the appealing flight analogy:

>We can think of the arrows in our Hasse diagrams as _one-way streets_ in two cities, \\(X\\) and \\(Y\\). And we can think of the blue dashed arrows as _one-way plane flights_ from cities in \\(X\\) to cities in \\(Y\\). Then \\(\Phi(x,y) = \text{true}\\) if we can get from \\(x \in X\\) to \\(y \in Y\\) _using any combination of streets and plane flights!_

Should "from cities in \\(X\\) to cities in \\(Y\\)" be "from streets in \\(X\\) to streets in \\(Y\\)" instead (as \\(X,Y\\) are already cities themselves)?

2 - In **Puzzle 174**:

>**Puzzle 174.** Suppose \\(g: Y \to X \\) is a monotone function from \\(X\\) to \\(Y\\)...

Should this be a function from \\(Y\\) to \\(X\\) instead?

1 - In the appealing flight analogy:

>We can think of the arrows in our Hasse diagrams as _one-way streets_ in two cities, \\(X\\) and \\(Y\\). And we can think of the blue dashed arrows as _one-way plane flights_ from cities in \\(X\\) to cities in \\(Y\\). Then \\(\Phi(x,y) = \text{true}\\) if we can get from \\(x \in X\\) to \\(y \in Y\\) _using any combination of streets and plane flights!_

Should "from cities in \\(X\\) to cities in \\(Y\\)" be "from streets in \\(X\\) to streets in \\(Y\\)" instead (as \\(X,Y\\) are already cities themselves)?

2 - In **Puzzle 174**:

>**Puzzle 174.** Suppose \\(g: Y \to X \\) is a monotone function from \\(X\\) to \\(Y\\)...

Should this be a function from \\(Y\\) to \\(X\\) instead?