If 𝑆𝑆 is a set with |𝑆|=3|𝑆|=3, what is |𝑆×(𝑆)||𝑆×𝑃(𝑆)|?

The notation |S| refers to the cardinality of set S, which is the number of elements in the set. In this case, |S| = 3, meaning that there are 3 elements in set S.

The notation P(S) refers to the power set of S, which is the set of all possible subsets of S, including the empty set and S itself. For a set with n elements, the power set will have 2^n elements. So, for set S with 3 elements, P(S) will have 2^3 = 8 elements.

The notation S x P(S) refers to the Cartesian product of S and P(S), which is the set of all ordered pairs (s, p) where s is an element of S and p is an element of P(S). The cardinality of the Cartesian product of two sets is the product of the cardinalities of the two sets. So, |S x P(S)| = |S| * |P(S)| = 3 * 8 = 24.

So, |S x P(S)| = 24.