Given that €={10,11,12,13,14,15......,30}
A= {Multiples of 5}
B={prime number of 10,11,12,13,14,15...,30}
C={odd number}
Find the element of:
a. A u B u C
b. A u B n C
c. A' n B n C
a. A u B u C:
To find the elements of A u B u C, we need to combine the elements from sets A, B, and C without duplication.
Elements of set A: {10, 15, 20, 25, 30}
Elements of set B: {11, 13, 17, 19, 23, 29}
Elements of set C: {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
Combining all the elements without duplication, we get:
{10, 11, 13, 15, 17, 19, 20, 21, 23, 25, 27, 29, 30}
b. A u B n C:
To find the elements of A u B n C, we need to combine the elements of sets A and B, while including only the elements that are also in set C.
Elements of set A: {10, 15, 20, 25, 30}
Elements of set B: {11, 13, 17, 19, 23, 29}
Elements of set C: {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
Finding the common elements in A, B, and C, we get:
{15, 17, 19, 23, 25, 29}
c. A' n B n C:
To find the elements of A' n B n C, we need to find the elements that are not in set A, but are present in both sets B and C.
Elements of set A: {10, 15, 20, 25, 30}
Elements of set B: {11, 13, 17, 19, 23, 29}
Elements of set C: {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
Finding the elements not in A, but present in B and C, we get:
{11, 13, 17, 19, 23, 29}
To find the elements of the given sets, let's go step by step:
a. To find the elements of A ∪ B ∪ C (the union of A, B, and C):
1. A = {Multiples of 5} = {10, 15, 20, 25, 30}
2. B = {Prime numbers of 10, 11, 12, 13, 14, 15, ..., 30} = {11, 13, 17, 19, 23, 29}
3. C = {Odd numbers} = {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
Now, let's combine all the elements from A, B, and C without repetitions:
A ∪ B ∪ C = {10, 11, 13, 15, 17, 19, 20, 21, 23, 25, 27, 29, 30}
Therefore, the elements of A ∪ B ∪ C are 10, 11, 13, 15, 17, 19, 20, 21, 23, 25, 27, 29, and 30.
b. To find the elements of A ∪ B ∩ C (the union of A, B, and C):
1. A = {Multiples of 5} = {10, 15, 20, 25, 30}
2. B = {Prime numbers of 10, 11, 12, 13, 14, 15, ..., 30} = {11, 13, 17, 19, 23, 29}
3. C = {Odd numbers} = {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
Now, let's find the elements that are common to A, B, and C:
A ∪ B ∩ C = {11, 13, 15, 17, 19, 23, 29}
Therefore, the elements of A ∪ B ∩ C are 11, 13, 15, 17, 19, 23, and 29.
c. To find the elements of A' ∩ B ∩ C (the complement of A, and the intersection of B and C):
1. A = {Multiples of 5} = {10, 15, 20, 25, 30}
2. B = {Prime numbers of 10, 11, 12, 13, 14, 15, ..., 30} = {11, 13, 17, 19, 23, 29}
3. C = {Odd numbers} = {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
To find the complement of A, we need to find the elements that are not in set A:
A' = {Elements not in A from the given set €} = {11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29}
Now, let's find the common elements between A', B, and C:
A' ∩ B ∩ C = {11, 13, 17, 19, 23, 29}
Therefore, the elements of A' ∩ B ∩ C are 11, 13, 17, 19, 23, and 29.