Venn Diagram Maker
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A Venn diagram draws each set as a circle, so shared elements sit where circles overlap. With A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, the overlap A ∩ B is {3, 4} and the union A ∪ B is {1, 2, 3, 4, 5, 6}.
Use u for union, n for intersection, – for difference, ‘ for complement, d for symmetric difference. Examples: A u B, A n B, (A u B)’, A – (B n C).
Green: the region A ∩ B′.
| Sets | |
| Shaded: A ∩ B′ (2) | {1, 2} |
| A (4) | {1, 2, 3, 4} |
| B (4) | {3, 4, 5, 6} |
| U (8) | {1, 2, 3, 4, 5, 6, 7, 8} |
| Operations | |
| A ∪ B (6) | {1, 2, 3, 4, 5, 6} |
| A ∩ B (2) | {3, 4} |
| A − B (2) | {1, 2} |
| B − A (2) | {5, 6} |
| A Δ B (4) | {1, 2, 5, 6} |
| A′ (complement in U) (4) | {5, 6, 7, 8} |
Show steps
- Inclusion–exclusion: |A ∪ B| = |A| + |B| − |A ∩ B| = 4 + 4 − 2 = 6.
How to use the Venn diagram maker
- Type the elements of A and B, separated by commas. Add C for a three-circle diagram.
- Optionally add a universal set U (needed for complements).
- Type a region such as A n B’ to shade it, then press Draw.
Set notation cheat sheet
| Symbol | Name | Meaning | Type here |
|---|---|---|---|
| A ∪ B | union | in A or B (or both) | A u B |
| A ∩ B | intersection | in both A and B | A n B |
| A − B | difference | in A but not B | A – B |
| A′ | complement | in U but not in A | A’ |
| A Δ B | symmetric difference | in exactly one | A d B |
Counting with Venn diagrams
The inclusion–exclusion principle: \(|A \cup B| = |A| + |B| – |A \cap B|\). For three sets, \(|A \cup B \cup C| = |A| + |B| + |C| – |A \cap B| – |A \cap C| – |B \cap C| + |A \cap B \cap C|\). Example: 30 students take art, 25 music, 10 both. Then 30 + 25 − 10 = 45 take at least one.
Venn diagrams in probability
Shaded areas also represent events. P(A or B) = P(A) + P(B) − P(A and B), the same subtraction as in counting, because the overlap is counted twice.
Venn diagram and sets quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
How do you make a Venn diagram?
Draw a rectangle for the universal set and a circle for each set, overlapping them. Put each element in the region for the sets it belongs to. This maker does it automatically.
How do I shade A ∩ B′?
Type A n B' in the shading box. It shades the part of A that is outside B.
Can I make a three-circle Venn diagram?
Yes. Enter elements in Set C. The diagram switches to three circles with all seven regions.
Why do I need a universal set?
Complements such as A′ mean “everything not in A,” which only makes sense relative to a universal set U.
Can I use words instead of numbers?
Yes. Any comma-separated items work, such as animals, names or letters.
Sources
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