Download Venn Diagrams [from Google Images] If you are a really cool

Venn Diagrams [from Google Images]
If you are a really cool mathematician you get to
have your name on a theorem like Rolle, or have
your name on a triangle like Pascal, or even your
name on a diagram like John Venn.
From Mental Floss
From Snorg Tees
From Google Images
From Google Images:
As you can probably guess, IB loves Venn
diagrams! So we should become experts.
All Venn diagrams have the same set-up:
A rectangle which can represent a sample space
Circle(s) which can represent events
This picture is from our textbook
The complement of A, indicated by A’, represents
the non-occurrence of event A. So the Venn
diagram can look like:
Since we can represent a sample space with a set,
then set notation is used with Venn diagrams.
x ∈ A is read as “x is an element of set A”
n (A) is read as “the number of elements in set A”
When there is more than one circle in the Venn
diagram, then we can be concerned with the union
of the sets and the intersection of the sets.
I can remember the “union” starts with the letter
“u” and the union symbol looks like a “u” ∪
[And it is a good thing to be united, so we should
smile!]
I don’t have a clever way to remember the
“intersection” symbol. Sorry! ∩
If two sets have no elements in common, then
they are considered to be disjoint sets.
This means that A ∩ B = Ø
Note: Ø is the symbol for the empty set so don’t
use it if you mean “zero”.
If A ∩ B = Ø, then A and B are said to be
“mutually exclusive”.
Note: Our textbook says that it is impossible to
represent independent events on a Venn diagram.
We can have more than two circles. Here is
Wikipedia’s look at Venn diagrams with more than
two events:
An example from our textbook:
One way to figure out how to fill in the Venn
Diagram:
50 married men were asked whether they gave
their wife flowers or chocolates for their last
birthday. [I got a pink Blackberry.] The results
were: 31 gave chocolates, 12 gave flowers, and 5
gave both chocolates and flowers. If one of the
married men was chosen at random, determine
the probability that he gave his wife:
(a) chocolates or flowers
(b) chocolates but not flowers
(c) neither chocolates nor flowers
(d) flowers if it is known that he did not give her
chocolates
First construct a Venn Diagram to illustrate the
problem.
Let
= number who gave chocolates
Let
= number who gave flowers
Another example:
Suppose S = x : x < 100 and x ∈ Z +
{
}
Let A = multiples of 7 in S
And B = multiples of 5 in S
Find the number of elements in the following
(a) A
(b) B
(c) A ∩ B
(d) A ∪ B
Can we find a shortcut to find (d)? [Use parts, a,
b, and c]