The following examples
should help you understand the notation, terminology, and concepts related
to Venn diagrams and set
notation.

Let's say that our universe
contains the numbers 1,
2,
3,
and 4.
Let A be
the set containing the numbers 1
and 2;
that is, A =
{1, 2}. (Warning: The
curly braces are the customary notation for sets. Do not use parentheses
or square brackets.) Let B be
the set containing the numbers 2 and
3;
that is, B
= {2, 3}. Then we have
the following relationships, with pinkish shading marking the solution
"regions" in the Venn diagrams:

set
notation

pronunciation

meaning

Venn
diagram

answer

A
U B

"A
union B"

everything that
is in either of the sets

{1, 2, 3}

A
^ B or

"A
intersect B"

only the things that
are in both of the sets

{2}

A^{c}or
~A

"A
complement", or "not
A"

everything in
the universe outside of
A

{3, 4}

A
– B

"A
minus B",
or "A
complement B"

everything in
A except
for anything in its overlap with
B

{1}

~(A
U
B)

"not
(A
union B)"

everything outside
A and
B

{4}

~(A
^ B) or ~()

"not
(A
intersect B)"

everything outside
of the overlap of A
and B

{1, 3, 4}

There are gazillions of
other possibilities for set combinations and relationships, but these
are among the simplest and most common. Note that different texts use
different set notation, so you should not be at all surprised if your
text uses still other symbols than those used above. But while the notation
may differ, the concepts will be the same. By the way, as you probably
noticed, your Venn-diagram "circles" don't have to be perfectly
round; ellipses will do just fine.

The intersection of
A
and C
is just the overlap between those two circles, so:

Given the following
Venn diagram, shade inAU(B–C).

As usual when faced with
parentheses,
I'll work from the inside out.

I'll first find
B
–
C.
"B
complement
C"
means I take B and
then throw out its overlap with C,
which gives me this:

Now I have to union this with A:

Note that unioning with
A put
some of C (that
is, some of what I'd cut out when I did "B
– C")
back into the answer. This is okay. Just because we threw out C
at one point, doesn't mean
that it all has to stay out forever.