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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 ( ) 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, .

Thus operations [1], [2], [3] work.

**Answer: (D) [1], [2], [3]**

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