Answer
(AUB)'∩C={4,6}
Work Step by Step
U={1,2,3,4,5,6,7}
A={1,3,5,7}
B={1,2,3}
C={2,3,4,5,6}
To find (AUB)'∩C, we need to find (AUB)'.
AUB={1,3,5,7}U{1,2,3} = {1,2,3,5,7}
(List of all elements of A and the elements of B that are not in A)
(AUB)' represents all the elements of U that are not in (AUB).
so (AUB)'={4,6}
(AUB)'∩C={4,6} ∩ {2,3,4,5,6} = {4,6}
(Common elements of (AUB)' and C)
