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.