It is given that E = {11, 13, 15, 17} and F = {12, 14, 15, 16, 17, 18, 20}.
(i) Draw a Venn diagram to represent the sets E and F.
(ii) From the Venn diagram, list all the elements in E ∪ F in set notation.
Answer (1)
In this task, we are asked to use a Venn diagram to represent two sets and identify the union of these sets.
Step 1: Understanding Sets E and F
Set E is given as E = { 11 , 13 , 15 , 17 } .
Set F is given as F = { 12 , 14 , 15 , 16 , 17 , 18 , 20 } .
Step 2: Drawing the Venn Diagram
To draw the Venn diagram:
Create two overlapping circles. Label one circle as Set E and the other as Set F.
Identify the common elements between the two sets, which are the elements that both sets share. These will go in the overlapping area of the circles. Here, the common elements are { 15 , 17 } .
Place the unique elements of Set E in the non-overlapping part of the circle labeled E. These are { 11 , 13 } .
Place the unique elements of Set F in the non-overlapping part of the circle labeled F. These are { 12 , 14 , 16 , 18 , 20 } .
Step 3: Finding the Union of E and F
The union of two sets E and F , denoted as E ∪ F , includes all elements that are in Set E, Set F, or in both.
From the Venn diagram, E ∪ F is given by collecting all unique elements: E ∪ F = { 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 20 }
Conclusion
Thus, the elements of the union E ∪ F listed in set notation are { 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 20 } . This process helps visually organize and understand the relationship between elements in the two sets.
