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 $352]$

$[$MA $3$ x $2]$

$[$MA $[$MA $352][$MA $11][$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.