Question

the following table lists the ages and number of players per age group that are on a baseball team. Let A= baseball players who are younger than 9 years oldhow many players are in the complement of A?

Answer 1

The complement of A, representing baseball players younger than 9 years old, includes players who are 9 years old and older. In this specific case, there are 6 players in the complement of A, as there are 4 players aged 9 and 2 players aged 10.

The complement of the set A, denoted as A^c, includes all elements that are not in A. In this context, A represents baseball players younger than 9 years old. The age groups provided are 7, 8, 9, and 10 years old. Therefore, the complement of A includes players who are 9 years old and older.

Let's calculate the complement by summing the number of players in age groups 9 and 10:

Number of players in A^c = Number of players aged 9 + Number of players aged 10 = 4 + 2 = 6

So, there are 6 players in the complement of A, which means there are 6 players who are 9 years old or older.

Answer 2

Given the table as shown in the question

We let A = baseball players who are younger than 9 years old

We want to find

`n(A^c)`

I.e The cardinality of A complement

Solution

From the table, it is clear that

`n(A)=8+3=11`

Therefore,

`n(A^c)=4+2=6`

Therefore, the number of players in the complement of A is 6