a) A∩B this symbol means the intersection between A and B, in the Venn diagram, is represented by the crossing between the two circles.
According to the diagram there are 9 cardinalities shared by both circles so
A∩B= 9
b) A∪B is the union between both events, it means that you are looking for the cardinalities that are included in A or B but not both, symbolically this is:
A∪B= A + B - A∩B
The total cardinalities included in A are 5 + 9= 14
The total cardinalities included in B are 6 + 9= 15
Note that the elements in the intersection are included in both circles, meaning that they will be counted twice, this is why you have to subtract it.
A∪B= A + B - A∩B= 14 + 15 - 9= 20
c) A∩B'
B' is the complement of B, this means that it includes all elements of U that are not included in B.
If U= 23 and B= 15 then B'= U - B= 23-15= 8
The cardinalities included in A∩B'=5
d) A'∩B
A' is the complement of A and includes all cardinalities that are outside that circle.
To know how many those are you have to do the same calculation as you did in the item before:
A'= U-A= 23-14= 9
From those 9 cardinalities only 6 are shared by both A' and B so,
A'∩B=6
e) A'∩B'
A'= 9
B'= 8
A'∩B'= 9+8= 17
