### Video Transcript

Which of the following choices is
not an empty set? The set of odd numbers between, but
not including, five and six. The set of whole numbers between,
but not including, five and six. The set of odd numbers between, but
not including, five and 27. Or, the set of even numbers
between, but not including, five and six.

Another word for an empty set is a
null set. As the name describes, this is a
set that doesn’t have any elements in it. It’s empty. The question gives us four possible
choices. Three of them are empty sets. We need to find the choice that is
not an empty set. Which set contains numbers? Let’s go through our choices one by
one.

Our first set is the set of odd
numbers between, but not including, five and six. The phrase but not including is
important here. We can’t include five or six in our
set. So, how many odd numbers are there
in between the numbers five and six? Well, there aren’t any numbers. Five and six are consecutive
numbers. They’re next door to each
other. There aren’t any odd numbers in
between. And so, we know that this first set
is going to be an empty set.

In our second choice, we’re given
some numbers in between five and six again, the set of whole numbers between, but
not including, five and six. So again, we can’t include the
numbers five and six in our answer. How many whole numbers are there in
between five and six? Well, for the same reasons as
before, there aren’t any whole numbers. Five and six are numbers that are
next to each other. The only numbers in between are
decimals. So, the set of whole numbers
between, but not including, five and six is another empty set.

For our third choice, we’re going
to need to sketch a longer number line, the set of odd numbers between, but not
including, five and 27. This number line shows values from
five to 30. And we need to consider all the odd
members between five and 27. So, let’s mark those two numbers on
our number line. Here’s number five, and here’s
where the number 27 is. Now as with all the other choices,
we’re not allowed to include these numbers in our set.

But there are some other odd
numbers that we can include, all the odd numbers that belong in between five and
27. What are they? They’re the numbers seven, nine,
11, 13, 15, 17, 19, 21, 23, and 25. This set contains 10 different
numbers or 10 elements. The set of odd numbers between, but
not including, five and 27 is a set that includes the elements seven, nine, 11, 13,
15, 17, 19, 21, 23, and 25. This choice is not an empty
set.

So, although we think we’ve found
the answer, let’s just check the final choice. And we’re back here to thinking of
numbers in between five and six again, the set of even numbers between, but not
including, five and six. And, of course, there are no even
numbers in between five and six if we’re not allowed to include six. So, this set is an empty set. The set that is not an empty set is
the one that contains 10 different elements. And this is the set of odd numbers
between, but not including, five and 27.