Question

The numerals represent cardinalities in the Venn diagram,3$6B(a) Find the cardinality of the set AB(b) Find the cardinality of the set AUB(c) Find the cardinality of the set ANB'.(d) Find the cardinality of the set A'nB.(e) Find the cardinality of the set A' B'.U(a) The cardinality of A NB is(b) The cardinality of A UB is(c) The cardinality ofAB' is(d) The cardinality of A' B isCor (e) The cardinality of A' B' is

Answer 1

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