Question

Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter R in the set of all months of the year.

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 set of all months of the year whose names do not contain the letter R in the set of all months of the year

The set \(X\) of all months of the year is,

\(X = \left\{ \begin{aligned}{l}{\rm{January}},\;{\rm{February}},\;{\rm{March}},\;{\rm{April}},\;{\rm{May}},\;{\rm{June}},\;{\rm{July}},\;{\rm{August}},\;\\{\rm{September}},\;{\rm{October}},\;{\rm{November}},\;{\rm{December}}\end{aligned} \right\}\)

It is required a subset \(Y\) of the months without the letter \(R\) of \(X\). The required set will be as follows:

\(X = \left\{ {{\rm{May}},\;{\rm{June}},\;{\rm{July}},\;{\rm{August}}} \right\}\)

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

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

The months 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: