Question

which of the following gives all of the sets that contain $-\frac{1}{2}$?
the set of all natural numbers, the set of rational numbers, and the set of all real numbers
the set of all integers and the set of rational numbers
the set of all rational numbers and the set of all real numbers
the set of all natural numbers and the set of all irrational numbers

Explanation:

First, classify $-\frac{1}{2}$: it is a rational number (can be written as a ratio of two integers, $-1$ and $2$), and all rational numbers are real numbers. Natural numbers are positive integers (1,2,3,...) so they do not include $-\frac{1}{2}$, and integers are whole numbers (..., -2, -1, 0, 1, ...) so they also exclude $-\frac{1}{2}$. Irrational numbers cannot be written as a ratio of integers, so $-\frac{1}{2}$ is not irrational. The only sets that contain $-\frac{1}{2}$ are the set of rational numbers and the set of real numbers.

Answer:

the set of all rational numbers and the set of all real numbers