Question

(a) use the names of the sets to label the regions of the venn diagram. names of the sets

Explanation:

Step1: Identify the out - most set

The out - most set is the set of all real numbers which is divided into two main subsets: rational and irrational numbers. Here, the large rectangle can be considered as the set of real numbers. The left part (inside the green border) represents rational numbers and the right part (inside the red border) represents irrational numbers.

Step2: Analyze the nested sets

Among rational numbers, integers are a subset. Whole numbers are non - negative integers, so they are a subset of integers. The innermost circle is rational numbers, the middle circle is integers and the outermost of these three nested circles is whole numbers.

Answer:

The large rectangle (entire diagram area) represents the set of real numbers. The right - hand side region (inside the red border) represents the set of irrational numbers. The left - hand side region (inside the green border) represents the set of rational numbers. Inside the set of rational numbers, the innermost circle represents the set of rational numbers, the middle circle represents the set of integers, and the outermost of these three nested circles represents the set of whole numbers.