### Video Transcript

Part a) A Venn diagram is shown
below. Which of the following represents
the shaded region on the Venn diagram? Is it A ∪ B dash, A dash ∩ B, A, or
B dash.

Before answering this specific
question, it is important to remember some of the notation for probability. Firstly, A dash means not A. This means that the fourth option B
dash means the area that is not in B. The u or union symbol in the first
option means “or.” This means that the first option
represents the area that is in A or not in B.

The n or intersection symbol means
“and” as seen in the second option. This demonstrates the area that is
not in A and in B. Whilst you might have spotted
already which one is the correct answer, let’s look at all four options and what
their Venn diagrams would look like.

Let’s firstly consider the third
option A. This consists of everything inside
the circle A. Clearly, this answer is
incorrect. Secondly, let’s look at B dash. This is the area of everything not
in B. This is the area of everything that
is not in circle B. Once again, this is clearly a wrong
answer.

The second option not A and B needs
to include the area that is not in A, but also in B. It must be outside of circle A, but
inside of circle B. This includes everything inside
circle B except the intersection or overlap between the two circles. It is clear from this that this is
the correct answer.

Whilst we have found the correct
answer, it is worth just confirming what A ∪ not B would look like. This is any area that is in A or
not in B. Firstly, we could circle the area
of A. We also need to shade any area left
that is not in B. This leaves us with an area similar
to but not exactly the same as the fourth option. Clearly, this is also
incorrect.

The shaded region on the Venn
diagram given is represented by not A ∩ B.

A different Venn diagram is shown
below. Which of the following represents
the shaded region on the Venn diagram? Is it not A ∪ B, is it not A ∩ not
B, is it A ∩ B, or is it not A ∩ B?

Once again, it is worth sketching
the four different options. The third option A ∩ B is the
overlap of circles A and circles B. Clearly, this is not the correct
answer. However, you might notice that the
correct answer is the exact opposite of this. Everything else is shaded except
the intersection. This means that the correct answer
is not A ∩ B.

This is shown in the fourth option
as it is everything that is not in the intersection. This means that the shaded region
on the Venn diagram is represented by not A ∩ B. Once again, we will shade the Venn
diagrams for the other two options for completeness.

The second option not A ∩ not B
involves shading everything that is not in circle A and not in circle B, everything
outside the two circles. Once again, this is clearly not
correct. The union of A and B is everything
inside circle A or inside circle B, everything contained within both circles. This means that not A ∪ B would be
everything outside the two circles.

This means that the notation in
option one and option two would give the same shaded region, both of which are
incorrect. In this part of the question, the
fourth option was correct.