I'll solve this Venn diagram problem step by step. Let me first examine the image to understand what's being asked.
Looking at the image, I can see it's a worksheet titled "Venn Diagram - Two Circles" with three different Venn diagrams. For each diagram, I need to fill in the blanks using the given Venn diagrams by calculating set operations like union (A ∪ B), intersection (A ∩ B), difference (B - A), etc.
Let me start with the first Venn diagram (top one) which shows sets A and B.
For the first diagram:
- Set A contains: 1, 2, 4, 5
- Set B contains: 2, 3, 4, 6
Now I'll calculate each required operation:
1. A ∪ B (union of A and B): All elements that are in A or B or both
A ∪ B = {1, 2, 3, 4, 5, 6}
2. A ∩ B (intersection of A and B): Elements that are in both A and B
A ∩ B = {2, 4}
3. A - B (elements in A but not in B):
A - B = {1, 5}
4. B - A (elements in B but not in A):
B - A = {3, 6}
Let me move to the second Venn diagram (middle one) which shows sets C and D.
For the second diagram:
- Set C contains: 5, 6, 7, 8
- Set D contains: 6, 7, 9, 10
Calculating each operation:
1. C ∪ D (union of C and D): All elements that are in C or D or both
C ∪ D = {5, 6, 7, 8, 9, 10}
2. C ∩ D (intersection of C and D): Elements that are in both C and D
C ∩ D = {6, 7}
3. C - D (elements in C but not in D):
C - D = {5, 8}
4. D - C (elements in D but not in C):
D - C = {9, 10}
Finally, let me work on the third Venn diagram (bottom one) which shows sets E and F.
For the third diagram:
- Set E contains: 1, 2, 3, 4, 5
- Set F contains: 3, 4, 5, 6, 7
Calculating each operation:
1. E ∪ F (union of E and F): All elements that are in E or F or both
E ∪ F = {1, 2, 3, 4, 5, 6, 7}
2. E ∩ F (intersection of E and F): Elements that are in both E and F
E ∩ F = {3, 4, 5}
3. E - F (elements in E but not in F):
E - F = {1, 2}
4. F - E (elements in F but not in E):
F - E = {6, 7}
I've now solved all the problems on the worksheet. Let me summarize the answers:
First Diagram (Sets A & B):
- A ∪ B = {1, 2, 3, 4, 5, 6}
- A ∩ B = {2, 4}
- A - B = {1, 5}
- B - A = {3, 6}
Second Diagram (Sets C & D):
- C ∪ D = {5, 6, 7, 8, 9, 10}
- C ∩ D = {6, 7}
- C - D = {5, 8}
- D - C = {9, 10}
Third Diagram (Sets E & F):
- E ∪ F = {1, 2, 3, 4, 5, 6, 7}
- E ∩ F = {3, 4, 5}
- E - F = {1, 2}
- F - E = {6, 7}
Parent Tip: Review the logic above to help your child master the concept of union and intersection of sets worksheet.