Chapter 3.8, Problem 23PPE

To determine

To draw: a Venn diagram to represent the union and intersection of the sets with the help of given sets.

Answer to Problem 23PPE

The Venn diagram that represents the intersection and union of the given sets is:

Explanation of Solution

Given information:

  $B=\{x\mid x$ is a positive, composite number less than 10}, $F=\{1,2,4,5,6,8,9\}$

  $G=\{x\mid x$ is a positive, oven number less than or equal to 10}.

Calculation:

The intersection of two sets $A$ and $B$ is the set that contains all elements of $A$ that also belong to $B$ , but no other elements. In other words, an element is in the intersection if it belongs to all of the sets. That is,

  $A\cap B=\{x\mid x\in A$

  $x\in B\}$

The union of two sets $A$ and $B$ is the collection of points which are in $A$ or in $B$ or in both $A$ and $B$ In other words, an element is in the union if it belongs to at least one of the sets. That is,

  $A\cup B=\{x\mid x\in A$

  $x\in B\}$

The given sets are below:

  $E=\{2,3,4,5,6,7,8,9\}$

  $F=\{1,2,4,5,6,8,9\}$

  $G=\{2,4,6,8,10\}$

The common elements of the sets $E$ , $F$ and $G$ are 2, 4, 6 and 8 which belongs to the intersection of three sets.

The common elements of the sets $E$ and $F$ other than 2, 4, 6 and 8 are 5 and 9.

There are no common elements of the sets $E$ and $G$ other than 2, 4, 6 and 8.

There are no common elements of the sets $F$ and $G$ other than 2, 4, 6 and 8.

Hence, the Venn diagram that represents the intersection and union of the given sets is below: