>>**Puzzle 78.** When we reason using transitivity:

>>\\(x \le y\\) and \\(y \le z\\) imply \\(x \le z\\)

>>what does this look like in terms of wiring diagrams?

It looks like horizontal composition. That is, that fact that one process can come after another (edit: but only if the first process's output is the second process's input).

>>**Puzzle 79.** When we reason using the monoidal preorder law:

>>\\(x \le x'\\) and \\(y \le y'\\) imply \\(x + y \le x' + y'\\)

>>what does this look like in terms of wiring diagrams?

It looks like vertical composition. That is, two processes can be done in parallel.

>>\\(x \le y\\) and \\(y \le z\\) imply \\(x \le z\\)

>>what does this look like in terms of wiring diagrams?

It looks like horizontal composition. That is, that fact that one process can come after another (edit: but only if the first process's output is the second process's input).

>>**Puzzle 79.** When we reason using the monoidal preorder law:

>>\\(x \le x'\\) and \\(y \le y'\\) imply \\(x + y \le x' + y'\\)

>>what does this look like in terms of wiring diagrams?

It looks like vertical composition. That is, two processes can be done in parallel.