Intersection of Solution Sets The intersection of two sets is the set of elements that are in both sets. It is represented by the symbol '∩'. For example,...
Intersection of Solution Sets
The intersection of two sets is the set of elements that are in both sets. It is represented by the symbol '∩'.
For example, let's consider the sets: A = {1, 3, 5} and B = {2, 4, 6}. The intersection of A and B would be the set {2, 3, 4}.
Properties of Intersection:
The intersection of two sets is a subset of the union of the two sets (A ∪ B = (A ∩ B)).
The intersection of two sets is commutative, meaning A ∩ B = B ∩ A.
The intersection of a set with itself is always the empty set, meaning A ∩ A = empty set.
Applications of Intersection:
Finding the intersection of two sets can help us solve linear inequalities.
For example, if we have the inequality 2x + 5 ≤ 13 and 3x - 1 ≥ 5, then the intersection of these two sets would be the set {3}.
Examples:
=> A ∩ B = {2, 4}
=> A ∩ B = {4}
Key Points:
Intersection is the set of elements that are in both sets.
Intersection is a subset of the union of the two sets.
Intersection is commutative.
Intersection of a set with itself is the empty set