# 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 ago

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H\T can also be written H - T.

- 3 years, 8 months ago

Ya ......dear right

- 3 years, 3 months ago

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

- 8 months, 3 weeks ago

Complement of H = H'

- 1 year, 10 months ago

this is kinda like logic gates

- 1 month, 1 week ago

Enlightening

- 4 months, 4 weeks ago

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

- 3 years, 9 months ago

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

- 3 years, 8 months ago