People and penguins can be in the part where the orange circle does not overlap with the blue circle. Mosquitoes have six legs and can fly, so the mosquito's point can be in the part where the blue circle does not overlap with the orange circle. Things that are not bipedal and can't fly (such as whales and rattlesnakes) can be represented by points outside these two circles. Technically, the above venn diagram can be interpreted as the connection between set A and set B, and they may have some (but not all) common elements.
The combination region of sets a and b is called the union of sets a and B. In this case, the union includes all bipeds, flying animals, bipeds and flying animals. Overlapping circles imply that the intersection of two sets is not empty-that is, in fact, there are creatures in the orange and blue circles at the same time.
Sometimes a box (called the Complete Works) is drawn outside venn diagram, indicating the space of all possible things. As mentioned above, whales can be represented as points that are not in the union but in the complete set (creatures or everything, depending on how you choose to define the complete set of a particular graph).
Note: it can also be used for ternary inclusion of a.b.c.3 units.
similar figures
Johnston diagram and Euler diagram may be consistent with Dow diagram in appearance. Any difference between them lies in their application fields, that is, in the types of separate complete works. Johnston diagram is especially suitable for the truth value of propositional logic, while Euler diagram shows a group of specific objects, and venn diagram's concept is more generally applicable to possible connections. The reason why venn diagram and Euler did not merge seems to be that Euler's version appeared as early as 100 years ago. Euler has made enough achievements, but Wayne only left such a diagram.
The difference between Otto and venn diagram is only in concept. Euler diagrams should show the connections between specific sets, while venn diagram should contain all possible combinations. The following is an example of Otto:
Setting a, b and c
In this example, one set is completely in another set. We say that group A is all the different kinds of cheese that can be found in the world, and group B is all the food that can be found in the world. From this picture, you can see that all cheese is food, but not all food is cheese. Furthermore, set C (such as a metal creation) and set B have no common elements (members of the set), from which we can logically assert that no cheese is a metal creation (and vice versa). Formally, the above figure can be mathematically interpreted as that set A is the proper subset of set B, while set C and set B have no common elements.
Or as a syllogism.
Expand to more collections
Many efforts have been made to extend venn diagram to multiple sets. Venn used ellipses to reach four sets, but he was never satisfied with his solution of five sets. A century ago, an elegant method was found to satisfy the Venn's informal standard about symmetric graphs. In the process of designing stained glass windows in memory of Wen En, A.W.F. Edwards put forward the' gear' method:
Three sets: Image: Edwards-ven-three.png.
Four sets: Image: Edwards-Venn-four.png.
Five sets: Image: Edwards-ven-five.png.
Six sets: Image: Edwards-Venn-six.png.
Quote: Another good math in ian stewart, you turned me into 1992 CH4.