Let U be the universal set and A, B, C, the subsets of U such that
U= {x|x £ Z; 0<x<=30}
A= {U{all primes}}, B= {all multiples of 3}, C= {1, 2, 5, 8, 9, 12, 15} . . .
Using the above information CN(AUB)^c
First, let's find AUB:
A= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
B= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}
AUB = {2, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 27, 29, 30}
Now, find the complement of AUB:
(AUB)^c = U - AUB
U = {1, 2, 3, ..., 30}
(AUB)^c = {1, 4, 8, 10, 14, 16, 20, 22, 25, 26, 28}
Finally, find the intersection of C and (AUB)^c:
C ∩ (AUB)^c = {8, 15}