A multidimensional array can be defined as an array whose elements are either multidimensional arrays or numbers and symbols. For example, the following are all legal multidimensional arrays: [MA 3 5 2] [MA 3 x 2] [MA [MA 3 5 2] [MA 1 1] [MA x y]] (a) (10 points) Define the set S which contains all multidimensional arrays in a bottom-up fashion. (b) (10 points) Give a grammar-based definition of the set of multidimensional arrays.