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?
- The natural numbers
- The integers
- The rational numbers
- The real numbers
- The complex numbers
- I, II, and III only
- II, III, and IV only
- III, IV, and V only
- II, III, IV, and V only
- 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.