Question

Use a Venn diagram to illustrate the subset of odd integers in the set of all positive integers not exceeding 10.

Short answer

The Venn diagram is,

Step-by-step solution

Definitions of Venn diagram

The Venn diagram is used to represent the universal set U, which contains all the objects under consideration.

Illustrate the subset of odd integers in the set of all positive integers not exceeding 10 by using Venn diagram

The set \(X\) of all positive integers not exceeding \(10\) is,

\(X = \left\{ {1,\;2,\;3,\;4,\;5,\;6,\;7,\;8,\;9,\;10} \right\}\)

It is required a subset \(Y\) of odd integers of \(X\). Therefore, \(Y\) containing only the odd integers in \(X\) are,

\(Y = \left\{ {1,\;3,\;5,\;7,\;9} \right\}\)

Since \(Y\) is a subset of \(X\), the Venn diagram of \(Y\) should be completely within the Venn diagram of \(X\).

The integers in the set of \(Y\) are added within the Venn diagram of \(Y\).

The integers in the set \(X\) that are not in the set \(Y\), are contain in the area that belongs to the Venn diagram of \(X\), but not to the Venn diagram of \(Y\).

Draw the Venn diagram as follows.