Draw a Venn diagram to represent the intersection and union of the sets: P = {1, 5, 7, 9, 13},
R = {1, 2, 3, 4, 5, 6, 7}, and Q = {1, 3, 5}.
show your work
Here is the Venn diagram representing the intersection and union of the sets P, R, and Q:
P = {1, 5, 7, 9, 13}
R = {1, 2, 3, 4, 5, 6, 7}
Q = {1, 3, 5}
The intersection (P ⋂ Q ⋂ R) is represented by the shaded area in the middle where all three sets overlap:
P ⋂ Q ⋂ R = {1, 5}
The union (P ⋃ Q ⋃ R) is represented by the entire area covered by the three sets combined:
P ⋃ Q ⋃ R = {1, 2, 3, 4, 5, 6, 7, 9, 13}
Note that the elements 2, 3, 4, 6, 7, 9, and 13 are not common to all three sets and are only part of the union.
To draw the Venn diagram representing the intersection and union of the sets P, R, and Q, follow these steps:
1. Draw a rectangle to represent the universal set, often denoted as U, which contains all the elements of P, R, and Q.
2. Inside the rectangle, draw three overlapping circles, each representing one of the sets: P, R, and Q. Make sure the circles intersect each other.
3. Label the circles as P, R, and Q.
4. Fill in the circles with the elements of the corresponding sets.
5. To represent the intersection of sets, fill in the region where the circles overlap. In this case, the overlapping region of circles P and R represents the elements common to both sets.
6. To represent the union of sets, fill in the entire area enclosed by the three circles. This represents all the elements present in any of the three sets.
Below is the step-by-step representation mentioned above:
Step 1:
__________
| |
| U |
|__________|
Step 2:
__________
| |
P | R |
| |
|__________|
\
\
Q
Step 3:
__________
| |
P | R |
| |
|__________|
\ .\
\ .
Q .
Step 4:
__________
| 1, 5, 7 |
P | 9, 13 |
|__________|
________
| 1, 3, 5 |
Q | |
|_________|
_______
R | |
| |
|_________|
Step 5 (Intersection):
__________
| |
P | R |
| |
|___ ___|
\. /
X
/.
/
Step 6 (Union):
__________
| 1, |
P | 5, 7 |
| 9, 13 |
|___ ___|
\. /
X
/.
/ \
| |
Q | 3 |
|_________|
_______
R | 2,4, |
| 6, |
|_________|
In this way, the Venn diagram is drawn to represent the intersection and union of sets P, R, and Q.
To draw a Venn diagram representing the intersection and union of sets P, R, and Q, first start by drawing three overlapping circles representing each set. Label one circle as P, one as R, and one as Q.
Next, we will determine the elements that belong to the intersection of sets P, R, and Q. The intersection of sets refers to the elements that are common to all three sets. To find this, look for the elements that are present in all three sets P, R, and Q. In this case, the only element that appears in all three sets is 1.
Now, place the element 1 in the region where all three circles overlap. This represents the intersection of sets P, R, and Q.
To find the elements that belong to the union of sets P, R, and Q, which represents all the elements in any of the three sets, look for all the elements in sets P, R, and Q and combine them. In this case, the union of sets P, R, and Q consists of the following elements: 1, 2, 3, 4, 5, 6, 7, 9, 13.
Now, place all these elements outside the intersection region, inside the individual circles. This represents the union of sets P, R, and Q.
Your completed Venn diagram should have the number 1 in the overlapping region of circles representing sets P, R, and Q, and the numbers 2, 3, 4, 5, 6, 7, 9, and 13 placed inside the individual circles representing sets P and/or R, but not Q.
For a visual representation, please refer to the link below:
[INSERT LINK TO VENN DIAGRAM]