Answer
Only C
Work Step by Step
First, perform the operation inside the parenthesis of the set\[\left( A\cup B \right)'\].
So we compute\[A\cup B\].
Set \[A\cup B\] contains all the elements which are either in set A or set B or in both.
In the Venn diagram,
Regions II, III, V and VI represent the set B.
Regions I, II, IV and V represent the set A.
Now the union of regions of set A and set B are I, II, III, IV, V and VI. So it represents the set\[A\cup B\].
To find the complement of the set\[A\cup B\], it contains all the elements of the universal set Uexcept the elements of set\[A\cup B\].
So region VII and VIII represent the set\[\left( A\cup B \right)'\].
Then common region of both the sets\[\left( A\cup B \right)'\]and C is region VII only.
So, region VII represents the set \[\left( A\cup B \right)'\cap C\]
Observe that it involved only set C. since region VII contains element of C only.
