Check that there is a symmetric monoidal structure on the power set of \(S\) ordered by subset relation. (The unit is \(S\) and product is \(\cap\))
Monotonicity: \(x_1 \subseteq y_1 \land x_2 \subseteq y_2 \implies x_1 \cap x_2 \subseteq y_1 \cap y_2\)
This is true: if something is in both \(x_1,x_2\), then it is in both \(y_1,y_2\), i.e. in their intersection.
Unitality: \(x \cap S = x = S \cap x\), since \(\forall x \in P(S): x \subseteq S\).
Associativity and symmetry come from associativity and symmetry of \(\cap\) operator.