Exercise 2.29

The monoidal unit must be \(false\) (satisfying the unitality condition (a)).

It’s not clear that the author is presenting these tables to show they are symmetric (as in “symmetric” monoidal preorder), but they show that symmetric condition (d) is satisfied.

The associative condition (c) is satisfied because booleans over \(\vee\) are associative.

The monotonicity requirement (a) is satisfied because the booleans over \(\vee\) are also already monotone, and this is apparent in the tables as well. See also Boolean algebra - Monotone laws and Monotonic function - In Boolean functions.