Which of the following sets of real numbers is such that if x is an element of the set and y is an element of the set, then the sum of x and y is an element of the set ?
I. The set of negative integers
II. The set of rational numbers
III. The set of irrational numbers

Options

A. None
B. I only
C. I and II only
D. II and III only

Answer

C

Explanation

Consider option I. The sum of two negative integers a negative integer. So option I will be part of the correct answer, eliminate (A) and (D).
Consider option II. The sum of two rational numbers is a rational number , eliminate (B).
Consider option III. The sum of two irrational numbers is not necessarily an irrational number. For example, the sum of the irrational number `3--sqrt(7)` and the irrational number `sqrt(7)` is 3, which is a rational number. Option III will not be part of the correct answer. (C ) is correct.