Question

let the universal set omega {0,1,2,3,4,5,6,7,8,9,10,11,12,14},then A ={0,2,3,4,5}, B={0,3,4,5,6,8,10} and C ={1,3,5,6,7,14} Find:
1.(A n B')'
2.A n (B n C)
3.omega'

Answer 1

1. (A ∩ B')'
In set theory, complement of a set is the set of elements that are not in the given set. So, B' (complement of B) will be {1,2,7,9,11,12,14}.
Thus, A ∩ B' = {2}, and its complement is {0,1,3,4,5,6,7,8,9,10,11,12,14}.

2. A ∩ (B ∩ C)
First, find B ∩ C:
B ∩ C = {3,5,6}.

Then, find A ∩ (B ∩ C):
A ∩ (B ∩ C) = {3,5}.

3. ω' (complement of omega)
Since omega includes all elements from 0 to 14, its complement (ω') will be an empty set {} as it includes no elements.