### Video Transcript

Given that π is a set containing
the elements seven, 11, and 22, π is a set containing the elements one, 11, 21, and
22, and π and π are subsets of some universal set π, which of the following could
be true? π is a set containing the element
22, π is a set containing the elements one, 11, and 21, π is a set containing the
elements one, seven, 11, and 21, or π is a set containing the elements one, seven,
11, 21, and 22.

This problem tests whether weβre
able to say what a possible universal set might contain if we know some of its
subsets. The question tells us that the
universal set that weβre talking about is π, and π and π are the subsets. Letβs represent this as a Venn
diagram. Letβs use this green square to
represent the universal set π. This orange circle can represent
set π. Notice that weβve drawn the circle
completely inside the square. This is because π is a subset of
the universal set π. Everything in π is inside π. And the numbers in π are seven,
11, and 22.

And we can also draw a pink circle
to represent set π, which is also a subset of the universal set. Now, when we look at the elements
of set π, we can see that two of the numbers are also in set π. So, when we draw our pink circle,
weβre going to have to make sure it overlapped with the orange one. So, the two numbers that both sets
share are 11 and 22. And then, as weβve said already,
set π contains the number seven too, and set π contains the numbers one and
21. So, this Venn diagram represents
the question.

Now, weβre given four statements
about the universal set, π. And weβre asked which of the
following could be true. Each statement gives the letter π
and then tells us what the elements of that universal set are. So, the correct answer is the one
that contains all the elements. When we look inside our green
square, we can see the numbers one, seven, 11, 21, and 22. This means that the correct answer
is the one that says π equals a set containing the elements one, seven, 11, 21, and
22, the five numbers that we can see inside the set.

Notice the word could in the last
question. Which of the following could be
true? The reason why it could be true,
and is not definitely true, is that the question doesnβt tell us that π and π are
the only things within the universal set π. If they were the only sets within
π, then this answer is correct. But of course, if there was another
set there, then we would need to include the numbers in that too. Universal sets contain everything
within them.

So, given that π is a set
containing the elements seven, 11, and 22, and π is a set containing the elements
one, 11, 21, and 22. And given that both π and π are
subsets of a universal set, which weβll call π. The statement that could be true is
that π is a set containing the elements one, seven, 11, 21, and 22.