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

1 answer

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}.