The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. The union is written as A∪B or “A or B”.
Intersection
The intersection of two sets is a new set that contains all of the elements that are in both sets. The intersection is written as A∩B or “A and B”.
The figure below shows the union and intersection for different configurations of two events in a sample space, using Venn diagrams.
Figure 14.1: The unions and intersections of different events. Note that in the middle column the intersection, A∩B, is empty since the two sets do not overlap. In the final column the union, A∪B, is equal to A and the intersection, A∩B, is equal to B since B is fully contained in A.
Exercise 14.4
A group of learners are given the following Venn diagram:
The sample space can be described as {n:nϵZ,1≤n≤15}.
They are asked to identify the event set of the intersection between event set A and event set B, also written as A∩B. They get stuck, and you offer to help them find it.
Which set best describes the event set of A∩B?
{7;10;11}
{1;2;3;4;5;6;7;9;10;11}
{1;2;3;4;5;6;7;9;10}
{7;10}
The intersection between event set A and event set B, also written as A∩B, can be shaded as follows:
Therefore the event set {7;10} best describes the event set of A∩B.
A group of learners are given the following Venn diagram:
The sample space can be described as {n:nϵZ,1≤n≤15}
They are asked to identify the event set of the union between event set A and event set B, also written as A∪B. They get stuck, and you offer to help them find it.
Which set best describes the event set of A∪B?
{1;6;7;10;15}
{1;2;4;5;6;7;8;9;10;11;12;13;14;15}
{2;4;5;9;10;11;12;13;14}
{3}
The union between event set A and event set B, also written as A∪B, can be shaded as follows:
Therefore the event set {1;2;4;5;6;7;8;9;10;11;12;13;14;15} best describes the event set of A∪B.