Union (A ∪ B)
Combine all elements
Intersection (A ∩ B)
Only common elements
1. Difference (A - B): Elements in A that are NOT in B.
2. Complement (A'): Everything in the Universal set (U) except A.
Formula: A' = U - A
3. De Morgan's Laws:
• (A ∪ B)' = A' ∩ B'
• (A ∩ B)' = A' ∪ B'
1. If A = {1, 2} and B = {2, 3}, find A ∪ B.
Answer: {1, 2, 3}. Union combines all elements from both sets.
2. If A = {1, 2} and B = {2, 3}, find A ∩ B.
Answer: {2}. Intersection identifies only the elements present in both sets.
3. What is A ∩ A' equal to?
Answer: ∅ (Empty set). A set and its complement never share any elements.
4. If U = {1, 2, 3, 4, 5} and A = {1, 2}, find A'.
Answer: {3, 4, 5}. The complement consists of everything in U that is NOT in A.
5. What are sets called if A ∩ B = ∅?
Answer: Disjoint Sets. They have no overlap.
6. Find A - B if A = {a, b, c} and B = {c, d}.
Answer: {a, b}. Start with A and remove anything that also appears in B.
7. Simplify (A')'.
Answer: A. The double complement brings you back to the original set.
8. According to De Morgan, (A ∪ B)' is equal to...
Answer: A' ∩ B'. The union flips to intersection when the complement moves inside.
9. If A ⊆ B, what is A ∪ B?
Answer: B. Since A is already inside B, combining them results in B.
10. What is A ∪ A' always equal to?
Answer: U (Universal Set). Together they cover every element in the universe.
11. Find B - A if A = {1, 2} and B = {2, 3}.
Answer: {3}. Elements in B that are not in A.
12. True or False: A - B is the same as B - A.
Answer: False. Order matters in set difference.
13. What is A ∩ U?
Answer: A. The common elements between a set and the universe is the set itself.
14. What is A ∪ ∅?
Answer: A. Adding nothing to A keeps it as A.
15. Simplify (A ∩ B)'.
Answer: A' ∪ B' (De Morgan’s second law).
16. If n(A)=5, n(B)=3, and A ∩ B = ∅, find n(A ∪ B).
Answer: 8. Since they are disjoint, simply add the counts (5 + 3).
17. Is A ∩ B a subset of A?
Answer: Yes. Every element in the intersection must be in A.
18. What is U'?
Answer: ∅. The "opposite" of everything is nothing.
19. If A ⊆ B, what is A - B?
Answer: ∅. If you take A and remove everything in B, nothing is left because A was completely inside B.
20. What is ∅'?
Answer: U. The complement of nothing is everything.