Try this beautiful problem from TOMATO Objective no. 27 based on Closure of a set of even numbers.
Problem: Closure of a set of even numbers
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 ($latex \frac {2}{4} = \frac{1}{2} $ ) or odd number ($latex \frac {12}{4} = 3 $) 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, $latex \frac { 4 + 6}{2} = 5 $.
Thus operations [1], [2], [3] work.
Answer: (D) [1], [2], [3]
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