Answer
Sets (AUB')' and A'∩B are equal. As the regions of both the sets are same.
Work Step by Step
Set A' represents all the regions belongs to universal set U that does not belongs to A
So, The regions III & IV represents the set A'.
Set B' represents all the regions belongs to universal set U that does not belongs to B
So, The regions I and IV represents the set B'.
a) Set AUB' represents all the regions of set A and set B'.
And (AUB')' represents the all the regions belongs to universal set U that does not belongs to (AUB').
So, The regions III represents the set (AUB')'.
a) Set A'∩B represents the common regions of set A' and B
So, The region III represents the set (A'∩B).
Based on parts a and b, sets (AUB')' and A'∩B are equal. As the regions of both the sets are same.
