Question

the following table lists the ages and number of players per age group that are on a volleyball team. let A = (volleyball players who are younger than 8 years old) how many players are in the complement of A?

Answer 1

The number of elements in the complement of a set A is the total number of elements in the universal set minus the number of elements in the set A.

It is given that A={volleyball players who are younger than 8 years old}.

From the table, volleyball players who are younger than the age of 8, are players who are 7 years old.

Hence, the number of players in A is 5.

Add the number of players for each age to get the total number of players:

$5+3+7+4=19\text{ players}$

It follows that the number of players in the complement of A is:

$19-5=14\text{ players}$

Hence, the number of players in the comp