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 n B n C
A u B n C
A' n B n C
A n B n C:
Multiples of 5: 10, 15, 20, 25
Prime numbers: 11, 13
Odd numbers: 11, 13, 15, 25
The elements that satisfy all three conditions are 11 and 13.
Therefore, A n B n C = {11, 13}.
A u B n C:
Multiples of 5: 10, 15, 20, 25
Prime numbers: 11, 13
Odd numbers: 11, 13, 15, 25
The elements that satisfy either A or B n C are 10, 11, 13, 15, 20, and 25.
Therefore, A u B n C = {10, 11, 13, 15, 20, 25}.
A' n B n C:
A' represents the complement of A, which includes all the numbers in the given set that are not multiples of 5.
The non-multiples of 5 in the given set are: 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30.
Prime numbers: 11, 13
Odd numbers: 11, 13, 17, 19, 21, 23, 27, 29
The elements that satisfy the conditions of A' n B n C are 11 and 13.
Therefore, A' n B n C = {11, 13}.
To find the elements of A ∩ B ∩ C:
1. List the elements of A:
A = {10, 15, 20, 25, 30}
2. List the elements of B (Prime numbers between 10 and 30):
B = {11, 13, 17, 19, 23, 29}
3. List the elements of C (Odd numbers between 10 and 30):
C = {11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
4. Find the common elements between A, B, and C:
A ∩ B ∩ C = {11, 13, 23, 29}
To find the elements of A ∪ B ∩ C:
1. Find the common elements between B and C:
B ∩ C = {11, 13, 17, 19, 23, 29}
2. Find the union of A and B ∩ C:
A ∪ (B ∩ C) = {10, 11, 13, 15, 17, 19, 20, 23, 25, 27, 29, 30}
To find the elements of A' ∩ B ∩ C:
1. Find the complement of A (numbers in € that are not multiples of 5):
A' = {11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29}
2. Find the common elements between A' (complement of A), B, and C:
A' ∩ B ∩ C = {11, 13, 23, 29}