# 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
4 years, 8 months ago

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H\T can also be written H - T.

- 4 years, 4 months ago

Ya ......dear right

- 3 years, 10 months ago

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

- 1 year, 4 months ago

Complement of H = H'

- 2 years, 6 months ago

this is kinda like logic gates

- 9 months, 1 week ago

Enlightening

- 1 year ago

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

- 4 years, 5 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?

- 5 months ago

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

- 4 years, 4 months ago