For every pair of natural numbers n and m

For every pair of natural numbers n and m, to which of the following sets must n + m belong?

  1. The natural numbers
  2. The integers
  3. The rational numbers
  4. The real numbers
  5. The complex numbers
  1. I, II, and III only
  2. II, III, and IV only
  3. III, IV, and V only
  4. II, III, IV, and V only
  5. I, II, III, IV, and V

Answer

The correct answer is E.

As n and m are both natural numbers, the sum of n and m is also a natural number.

Natural numbers are a subset of integers, integers are a subset of rational numbers, rational numbers are a subset of real numbers, and real numbers are a subset of complex numbers. Therefore, n + m belongs to the sets found in I, II, III, IV, and V.