Question

the venn diagram here shows the cardinality of each set. use this to find the cardinality of given set.
the number of elements in set a=
the number of elements in set a and set c=
the number of elements in set a or set c=
the number of elements that are not in set c=

Explanation:

Step1: Find the cardinality of set A

The cardinality of set A is the sum of all the regions within circle A. So, \(7 + 4+2 + 6=19\).

Step2: Find the cardinality of \(A\cap C\)

The intersection \(A\cap C\) is the sum of the regions common to both A and C. So, \(6 + 2=8\).

Step3: Find the cardinality of \(A\cup C\)

Using the formula \(n(A\cup C)=n(A)+n(C)-n(A\cap C)\).
First, find \(n(C)=8 + 6+2 + 7 = 23\).
Then \(n(A\cup C)=19+23 - 8=34\).

Step4: Find the number of elements not in set C

Sum all the regions not in circle C. So, \(7+4 + 6+3=20\).

Answer:

The number of elements in Set A = \(19\)
The number of elements in Set A and Set C = \(8\)
The number of elements in Set A or Set C = \(34\)
The number of elements that are not in Set C = \(20\)