Venn diagrams are a visual way of representing the properties of sets. The Venn diagrams most commonly encountered have three circles which overlap to create seven sections although there are actually many other types of Venn diagrams.
In examples used for teaching, the three-circle Venn diagrams are often used to display the result of a three-question survey such as the one in the table below. (Note that if you have one of the Duxbury braille fonts installed on your computer, you should see braille dots in the first column of the table; otherwise you will see ASCII Braille.)
| Braille Cell | 1. Like TV? | 2. Like sports? | 3. Like school? | How many persons? |
|---|---|---|---|---|
| L | yes | yes | yes | 5 |
| B | yes | yes | no | 3 |
| K | yes | no | yes | 1 |
| A | yes | no | no | 4 |
| 2 | no | yes | yes | 2 |
| 1 | no | yes | no | 9 |
| ' | no | no | yes | 7 |
If the information in the table is represented using a three-circle Venn diagram, each of the circles represents one of the questions as in the illustration below. The number of persons who answered "yes" to all three questions is placed in the central section where all three circles overlap. The number of persons who answered "yes" to any two of the questions is placed in the section where just the two circles corresponding to those two questions overlap. The number of persons who answered "yes" to only one of the questions is placed in the non-overlapping section of the corresponding circle.
My idea is that when first presenting the circles to a braille-reading student, it might be helpful to label the seven sections of the Venn diagram with those braille cells which have dots in the rows corresponding to the "yes" answers. That should help the student to appreciate the relationship between the table format and the diagram format.
