To determine the two code fragments that will allow the class to compile, let's go through each option:
Option A) foreach(x) System.out.println(z); - This option is incorrect because the "foreach" loop syntax is incorrect. It should be for (int z : x) to iterate through the elements of the x array.
Option B) for(int z : x) System.out.println(z); - This option is correct because it uses the enhanced "for" loop (also known as the "foreach" loop) to iterate through the elements of the x array. This syntax is valid and will allow the class to compile.
Option C) while( x.hasNext()) System.out.println( x.next()); - This option is incorrect because it assumes that x is an iterator object with the methods hasNext() and next(). However, in the given code, x is declared as a variable of type int[] (an array), which does not have these methods. Therefore, this option is incorrect.
Option D) for( int i=0; i< x.length; i++ ) System.out.println(x[i]); - This option is correct because it correctly uses a basic "for" loop to iterate through the elements of the x array. It initializes a counter variable i to 0, checks if i is less than the length of the array x, and increments i in each iteration. The syntax x[i] is used to access the elements of the array. This option is valid and will allow the class to compile.
Therefore, the correct options are B) for(int z : x) System.out.println(z); and D) for( int i=0; i< x.length; i++ ) System.out.println(x[i]);.