Understanding Sets and Set Operations
Sets are collections of distinct objects, considered as an object in their own right. The basic operations on sets include union, intersection, and complement.
- Union (A ∪ B): Combines all elements from both sets, removing duplicates.
- Intersection (A ∩ B): Contains only the elements that are in both sets.
- Complement (A'): Contains all elements not in set A, within a universal set.
To represent these operations:
- If A = {1, 2, 3} and B = {3, 4, 5}, then:
- Union: A ∪ B = {1, 2, 3, 4, 5}
- Intersection: A ∩ B = {3}
- Complement: If the universal set U = {1, 2, 3, 4, 5, 6}, then A' = {4, 5, 6}.
Understanding these operations is crucial for solving problems in set theory efficiently.
Key points to remember
- A set is a collection of distinct objects.
- Union combines elements from both sets.
- Intersection includes common elements only.
- Complement contains elements not in the set.
- Use correct notation for clarity in solutions.
Worked example
Given A = {2, 4, 6} and B = {4, 5, 6}, find A ∪ B and A ∩ B.
- A ∪ B = {2, 4, 5, 6}
- A ∩ B = {4, 6}