S is the set whose elements are zero and all even integers, positive and negative. Consider the 5 operations- [1] addition; [2] subtraction; [3] multiplication; [4] division; and [5] finding the Arithmetic Mean. Which of these operations applied to any pair of elements of S, yield only elements of S.

Solution:

Adding, subtracting and multiplying even numbers yield even numbers.

Division may yield non-integer ( ) or odd number () both of which are not members of S. So division is ruled out.

Finally arithmetic of two even numbers may be a odd number. For example, .