Final answer:
The set operations between sets A and B involve finding the intersection (A ∩ B), union (A ∪ B), difference (A - B), and the difference (B - A), with each resulting set containing the respective elements based on those operations.
Step-by-step explanation:
The student is provided with sets A and B which are subsets of set S, the set of all strings of 0's and 1's of length 4. To find the following operations:A intersection B (A ∩ B): This is the set containing elements that are in both set A and B. Therefore, A ∩ B = {0001}.A union B (A ∪ B): This represents all elements that are in either set A or B, or in both. Hence, A ∪ B = {0110, 0101, 1100, 0001, 1011, 1110, 1010}.A minus B (A - B): This is the set of elements in A that are not in B. Thus, A - B = {0110, 0101, 1100}.B minus A (B - A): This set contains elements in B that are not in A. Therefore, B - A = {1011, 1110, 1010}.(a) The set AB contains all outcomes that lie in both sets A and B. In this case, 0001 is the only outcome that is in both sets A and B. Therefore, AB = {0001}.
(b) The set AUB contains all outcomes that lie in either of the sets A or B. In this case, the outcomes in sets A and B are {0110, 0101, 1100, 0001} and {1011, 1110, 1010, 0001} respectively. So AUB = {0110, 0101, 1100, 0001, 1011, 1110, 1010}.(c) The set A - B contains all outcomes that are in set A but not in set B. In this case, the outcome 0110 is in set A but not in set B. So A - B = {0110}.(d) The set B - A contains all outcomes that are in set B but not in set A. In this case, the outcomes {1011, 1110, 1010} are in set B but not in set A. So B - A = {1011, 1110, 1010}.