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) AuB = (2,3,4,5,6,8,9,10)
ii) AnB = (2)
iii) BuC = (2,6,8,10)
iv) AnBnC = (2)
v) AnBuC = (2)
To find the requested sets, we must perform some operations on the given sets U, A, B, and C. Here are the step-by-step calculations:
i) A U B (Union of A and B):
To find the union of two sets, we combine all the elements from both sets while removing any duplicate elements.
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
Combining all elements from both sets while removing duplicates, we get:
A U B = (2, 3, 4, 5, 6, 8, 9, 10)
So, A U B = (2, 3, 4, 5, 6, 8, 9, 10).
ii) A n B (Intersection of A and B):
To find the intersection of two sets, we identify the common elements present in both sets.
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
The common elements in A and B are {2}. Therefore:
A n B = (2)
iii) B u C (Union of B and C):
To find the union of two sets, we combine all the elements from both sets while removing any duplicate elements.
B = (2, 6, 8, 10)
C = (2, 6, 10)
Combining all elements from both sets while removing duplicates, we get:
B u C = (2, 6, 8, 10)
So, B u C = (2, 6, 8, 10).
iv) A n B n C (Intersection of A, B, and C):
To find the intersection of three sets, we identify the common elements present in all three sets.
A = (2, 3, 4, 5, 9)
B = (2, 6, 8, 10)
C = (2, 6, 10)
The common elements in A, B, and C are {2}. Therefore:
A n B n C = (2)
v) A n B u C (Intersection of A and Union of B and C):
First, we find the union of sets B and C, then find the intersection of set A with this union.
B = (2, 6, 8, 10)
C = (2, 6, 10)
Combining all elements from both sets while removing duplicates, we get:
B u C = (2, 6, 8, 10)
Now, we find the intersection of A with this union set:
A = (2, 3, 4, 5, 9)
B u C = (2, 6, 8, 10)
The common elements in A and the union of B and C are {2}. Therefore:
A n B u C= (2)
I hope this helps! Let me know if you have any further questions.
To find the answers, we need to understand the set operations: union (AuB), intersection (AnB), and complement.
Given:
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}
i) AuB (Union of A and B):
The union of two sets A and B includes all elements that are in either A or B or both. To find the union, you can simply combine the elements of both sets, removing any duplicates.
A U B = {2, 3, 4, 5, 9, 6, 8, 10}
ii) AnB (Intersection of A and B):
The intersection of two sets A and B includes only the elements that are common to both A and B.
A n B = {2}
iii) BuC (Union of B and C):
To find the union of B and C:
B U C = {2, 6, 8, 10} (since 2, 6, 8, and 10 all appear in either B or C, or both)
iv) AnBnC (Intersection of A, B, and C):
To find the intersection of A, B, and C:
A n B n C = {} (there are no elements common to all of the sets A, B, and C)
v) AnBuC (Intersection of A, B, and C):
To find the intersection of A, B, and C:
A n B n C = {2} (as 2 is the only element common to all sets A, B, and C)
So:
i) A U B = {2, 3, 4, 5, 9, 6, 8, 10}
ii) A n B = {2}
iii) B U C = {2, 6, 8, 10}
iv) A n B n C = {}
v) A n B n C = {2}