# Venn Diagrams and Set Notation

A Venn Diagram is a way to visualize set relations between a finite number of sets. Below is a Venn Diagram for three sets $T, D,$ and $H$. Venn Diagram Sets

### We introduce some notation from Set Theory:

1. $|T|$ is the number of elements in set $T$.

2. Intersection of two sets, denoted $\cap$, refers to the elements that are in both sets. In the example, $T \cap D = \{ d, g\}$.

3. Union of two sets, denoted $\cup$, refers to the elements that are in at least one of the two sets. In the example, $T \cup H = \{a, c, d, e, f, g\}$.

4. Complement (Absolute), denoted $^c$, refers to the elements that are not in the set. In the example, $D^c = \{ a, c, e, i\}$.

5. Complement (Relative), denoted $\backslash$, refers to the elements in the first set, but are not in the second set. In the example, $H\backslash T = \{ c, f \}$.

6. Symmetric Difference, denoted $\triangle$, refers to the elements that are in at least one of the two sets, but are not in both sets. In the example, $D \triangle H = \{b, c, d, e\}$. Note by Arron Kau
6 years, 8 months ago

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H\T can also be written H - T.

- 6 years, 3 months ago

Ya ......dear right

- 5 years, 10 months ago

Complement of H = H'

- 4 years, 5 months ago

As a non-mathematician I found some of the thinking in these examples quite puzzling and hard to follow!

- 3 years, 3 months ago

The simplest things are the hardest :]

- 9 months, 3 weeks ago

how do you solve when there is an unknown is a given set?

- 6 years, 4 months ago

yeah,, idont find this post useful in solving,, please how do you actually solve???

- 6 years, 3 months ago

You need to turn the rules into English and use logic. Like in the question that you probably came from, it says that: 0 is in the set. If $p$ is in the set, and $q$ is in the set, and $p \neq q$, then $p+q$ is in the set. Now, if 10 is in the set, then -10 being in the set wouldn't break any rules, becuase $-10 \neq 10$ and $-10+10=0$ which is also in the set.

Set notation isn't useful in problem solving, but it helps show the question in a short way. Imagine if we didn't have any math symbols. Then $3x-9= 0, x=3$ would be: "Take a number. If you take away nine from 3 times that number the answer is zero. The number is 3." Which is easier to understand?

- 2 years, 4 months ago

Enlightening

- 3 years ago

this is kinda like logic gates

- 2 years, 8 months ago