Use the listing method to represent the following set. { x | x I, 2 ≤ x ≤ 5}
2 answers:
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Answer:
a) 25
b) 30
c) 10
d) Not Mozart, 6
e) 2
Step-by-step explanation:
We use a Venn Diagram to solve this question.
I am going to say that:
A are the students who like Mozart.
B are the students who like Beethoven
C are the students who like Haydn.
We have that:
In which a are those who only like Mozart, are those who like Mozart and Beethoven,
are those who like Mozart and Haydn and
are those who like all three of them.
By the same logic, we have that:
We start finding these values from the intersection:
8 like all three composers
This means that
14 like Beethoven and Haydn
This means that:
So
21 like Mozart and Haydn
This means that:
Then
14 like Mozart and Beethoven
This means that:
31 like Franz Joseph Haydn
This means that C = 31. So
36 like Ludwig van Beethoven
This means that
So
37 like Wolfgang Amadeus Mozart
This means that A = 37. Then
a. exactly two of these composers?
b. exactly one of these composers?
c. like only Mozart?
d. like Beethoven and Haydn, but not Beethoven?
I will use not Mozart.
So
Not Mozart, 6.
e. like none of these composers?
At least 1:
The total is 65
So 65 - 63 = 2 like none of these composers