1.4 - De Morgon's Law and Distributive Law.


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1.4.1 - De Morgon's Law.


1: According to De Morgan's Law, what is the complement of the union of two sets X and Y?
Correct Answer: B) X' ∩ Y'
2: According to De Morgan's Law, what is the complement of the intersection of two sets X and Y?
Correct Answer: B) X' ∪ Y'
3: Given U = {1,2,3,4,5,6}, A = {2,3}, and B = {3,4,5}, what is (A ∪ B)'?
Correct Answer: B) {1, 6}
4: Given U = {1,2,3,4,5,6}, A = {2,3}, and B = {3,4,5}, what is A' ∩ B'?
Correct Answer: D) {1, 6}
5: If A and B are two sets, what is the result of A ∩ (A ∪ B)'?
Correct Answer: C) ϕ
6: Which of the following represents the correct application of De Morgan’s Law for the complement of the intersection of two sets A and B?
Correct Answer: D) (A ∩ B)' = A' ∪ B'
7: Given U = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}, what is A' ∩ B'?
Correct Answer: D) {1, 6}

1.4.2 - Distributive Law.


8: According to the Distributive Law, what is A ∪ (B ∩ C) equivalent to?
Correct Answer: B) (A ∪ B) ∩ (A ∪ C)
9: According to the Distributive Law, what is A ∩ (B ∪ C) equivalent to?
Correct Answer: A) (A ∩ B) ∪ (A ∩ C)
10: If A = {1,2,3,6} and B = {2,4,6,8}, what is (A ∪ B)?
Correct Answer: A) {1,2,3,4,6,8}
11: For sets A = {1,2,3,6} and B = {2,4,6,8}, what is (A ∩ B)?
Correct Answer: A) {2,6}
12: Given A = {1,2,3,6}, B = {2,4,6,8}, and C = {1,3,5,7}, what is (A ∪ B) ∩ (A ∪ C)?
Correct Answer: A) {1,2,3,6}
13: Given A = {1,2,3,6}, B = {2,4,6,8}, and C = {1,3,5,7}, what is (A ∩ B) ∪ (A ∩ C)?
Correct Answer: A) {1,2,3,6}
14: Using the Distributive Law, what is (A ∩ B) ∪ (A - B)?
Correct Answer: A) A
15: To prove that A ∩ (A' ∪ B) = A ∩ B, which law is used?
Correct Answer: B) Distributive Law