U=(1,2,3,4,5,6,7,8,9,10)
A=(2,3,4,5,9)
B=(2,6,8,10)
C=(2,6,10)
Find i)AuB ii) AnB iii)BuC iv) AnBnC v) AnBuC
i) A∪B :
To find the union of sets A and B, we combine all the elements from both sets without duplicating any elements.
A∪B = (2,3,4,5,9,6,8,10)
ii) A∩B :
To find the intersection of sets A and B, we determine which elements are common to both sets.
A∩B = (2)
iii) B∪C :
To find the union of sets B and C, we combine all the elements from both sets without duplicating any elements.
B∪C = (2,6,8,10)
iv) A∩B∩C :
To find the intersection of sets A, B, and C, we determine which elements are common to all three sets.
A∩B∩C = (2)
v) A∪B∪C :
To find the union of sets A, B, and C, we combine all the elements from all three sets without duplicating any elements.
A∪B∪C = (2,3,4,5,9,6,8,10)
To find the set operations, we will use the following symbols:
- U: Universal set (all possible elements)
- A: Set A
- B: Set B
- C: Set C
- ∩: Intersection (elements in common between sets)
- ∪: Union (all elements in the sets combined)
i) A∪B
To find A∪B, we combine all the elements from both sets without duplicating any elements.
A= {2, 3, 4, 5, 9}
B= {2, 6, 8, 10}
A∪B= {2, 3, 4, 5, 6, 8, 9, 10}
ii) A∩B
To find A∩B, we determine the elements that are common to both sets A and B.
A= {2, 3, 4, 5, 9}
B= {2, 6, 8, 10}
A∩B= {2}
iii) B∪C
To find B∪C, we combine all the elements from both sets without duplicating any elements.
B= {2, 6, 8, 10}
C= {2, 6, 10}
B∪C= {2, 6, 8, 10}
iv) A∩B∩C
To find A∩B∩C, we determine the elements that are common to all three sets A, B, and C.
A= {2, 3, 4, 5, 9}
B= {2, 6, 8, 10}
C= {2, 6, 10}
A∩B∩C= {2}
v) A∪B∪C
To find A∪B∪C, we combine all the elements from all three sets without duplicating any elements.
A= {2, 3, 4, 5, 9}
B= {2, 6, 8, 10}
C= {2, 6, 10}
A∪B∪C= {2, 3, 4, 5, 6, 8, 9, 10}
I hope this clarifies the set operations for you!
To find the union (AuB), intersection (AnB), union (BuC), intersection (AnBnC), and intersection (AnBuC) of the given sets, follow these steps:
i) AuB (Union of A and B):
To find the union of sets A and B, combine all the elements from both sets removing any duplicates.
Solution:
U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
To find AuB, include all the elements from set A and set B:
AuB = (2, 3, 4, 5, 6, 8, 9, 10)
ii) AnB (Intersection of A and B):
To find the intersection of sets A and B, include only the elements that are common to both sets.
Solution:
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
To find AnB, include only the common elements:
AnB = (2)
iii) BuC (Union of B and C):
To find the union of sets B and C, combine all the elements from both sets removing any duplicates.
Solution:
B = (2, 6, 8, 10)
C = (2, 6, 10)
To find BuC, include all the elements from set B and set C:
BuC = (2, 6, 8, 10)
iv) AnBnC (Intersection of A, B, and C):
To find the intersection of sets A, B, and C, include only the elements that are common to all three sets.
Solution:
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
C = (2, 6, 10)
To find AnBnC, include only the common elements:
AnBnC = (2)
v) AnBuC (Intersection of A, B, and C):
To find the intersection of sets A, B, and C, include only the elements that are common to all three sets.
Solution:
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
C = (2, 6, 10)
To find AnBuC, include only the common elements:
AnBuC = (2)