Find the complement of set of U=(1,2,,3,4,5,6,7,8,9,10,11,12) A=(1,2,9) B=(1,6,8,10) C= (1,5,7,9)
To find the complement of a set, we consider the elements that are not in the set.
The complement of set A is denoted as A' and includes all the elements in the universal set U that are not in A.
A' = {3, 4, 5, 6, 7, 8, 10, 11, 12}
Similarly, the complement of set B, B', includes all the elements in the universal set U that are not in B.
B' = {2, 3, 4, 5, 7, 9, 11, 12}
The complement of set C, C', includes all the elements in the universal set U that are not in C.
C' = {2, 3, 4, 6, 8, 10, 11, 12}
To find the complement of a set, we need to find the elements that are not in the set.
Based on the given sets:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {1, 2, 9}
B = {1, 6, 8, 10}
C = {1, 5, 7, 9}
1. We start by finding the complement of set A.
The complement of A (A') contains all the elements in U that are not in A.
A' = U - A = {3, 4, 5, 6, 7, 8, 10, 11, 12}
2. Next, we find the complement of set B.
The complement of B (B') contains all the elements in U that are not in B.
B' = U - B = {2, 3, 4, 5, 7, 9, 11, 12}
3. Lastly, we find the complement of set C.
The complement of C (C') contains all the elements in U that are not in C.
C' = U - C = {2, 3, 4, 6, 8, 10, 11, 12}
Therefore, the complements of the given sets are:
A' = {3, 4, 5, 6, 7, 8, 10, 11, 12}
B' = {2, 3, 4, 5, 7, 9, 11, 12}
C' = {2, 3, 4, 6, 8, 10, 11, 12}
To find the complement of a set, we need to find all the elements in the universal set that are not in the original set.
Given:
Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Set A = {1, 2, 9}
Set B = {1, 6, 8, 10}
Set C = {1, 5, 7, 9}
To find the complement of set A, we need to find all the elements in the universal set U that are not in set A.
To do this, we can subtract set A from the universal set U using the set difference operation.
Complement of A = U - A
Performing the set difference operation:
Complement of A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} - {1, 2, 9}
Removing the common elements from both sets:
Complement of A = {3, 4, 5, 6, 7, 8, 10, 11, 12}
Therefore, the complement of set A is {3, 4, 5, 6, 7, 8, 10, 11, 12}.
Similarly, to find the complements of sets B and C, you can follow the same steps:
Complement of B = U - B
Complement of C = U - C
Performing the set difference operation for set B:
Complement of B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} - {1, 6, 8, 10}
Removing the common elements from both sets:
Complement of B = {2, 3, 4, 5, 7, 9, 11, 12}
Therefore, the complement of set B is {2, 3, 4, 5, 7, 9, 11, 12}.
Performing the set difference operation for set C:
Complement of C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} - {1, 5, 7, 9}
Removing the common elements from both sets:
Complement of C = {2, 3, 4, 6, 8, 10, 11, 12}
Therefore, the complement of set C is {2, 3, 4, 6, 8, 10, 11, 12}.