Question

use a venn diagram to illustrate the relationship between the given sets of numbers. 39. natural (n), integers (z), and rational (q) 40. whole (w)

Explanation:

A Venn diagram is a visual representation using circles to show relationships between sets. Natural numbers (N) are \(1, 2, 3,\cdots\). Whole numbers (W) are \(0, 1, 2,\cdots\). Integers (Z) are \(\cdots,- 2,-1,0,1,2,\cdots\). Rational numbers (Q) are numbers that can be written as \(\frac{a}{b}\), \(b
eq0\), \(a,b\in Z\). We know that \(N\subset W\subset Z\subset Q\). So we draw a large circle for \(Q\), inside it a smaller circle for \(Z\), inside \(Z\) a smaller circle for \(W\), and inside \(W\) a smaller circle for \(N\).

Answer:

Draw a large circle labeled \(Q\). Inside it, draw a smaller circle labeled \(Z\). Inside \(Z\), draw a smaller circle labeled \(W\). Inside \(W\), draw a smaller circle labeled \(N\).