Answer
a.) IV
b.) I, III IV
c.) no, the regions of (AUB)' and A'UB' are always different.
Work Step by Step
a) Set (AUB)' represents all the regions belongs to universal set U that does not belongs to AUB The regions IV belongs to the set (AUB)'.
b) 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'. The set A'UB' represents all the regions of set A' and set B'. So, The region I, III, IV represents A'UB'.
c) Based on parts a and b (AUB)' and A'UB' will never equal to each other, because the regions of (AUB)' and A'UB' are always different.
