what is a venn diagram?

Answer 1

Venn diagrams are illustrations used in the branch of mathematics known as set theory. They show all of the possible mathematical or logical relationships between sets (groups of things).

The orange circle (set A) might represent, for example, all living creatures which are two-legged. The blue circle, (set B) might represent living creatures which can fly. The area where the blue and orange circles overlap (which is called the intersection) contains all living creatures which both can fly and which have two legs — for example, parrots. (Imagine each separate type of creature as a point somewhere in the diagram.)

Humans and penguins would be in the orange circle, in the part which does not overlap with the blue circle. Mosquitos have six legs, and fly, so the point for mosquitos would be in the part of the blue circle which does not overlap with the orange one. Things which do not have two legs and cannot fly (for example, whales and rattlesnakes) would all be represented by points outside both circles. Technically, the Venn diagram above can be interpreted as "the relationships of set A and set B which may have some (but not all) elements in common".

The combined area of sets A and B is called the union of sets A and B. The union in this case contains all things which either have two legs, or which fly, or both.

The area in both A and B, where the two sets overlap, is defined as A∩B, that is A intersected with B. The intersection of the two sets is not empty, because the circles overlap, i.e. there are creatures that are in both the orange and blue circles.

Sometimes a rectangle called the Universal set is drawn around the Venn diagram to show the space of all possible things. As mentioned above, a whale would be represented by a point that is not in the union, but is in the Universe (of living creatures, or of all things, depending on how one chose to define the Universe for a particular diagram).

A Venn diagram is a diagram used to divide up two or more objects to view similarities and differences.

Extensions to higher numbers of sets
Venn diagrams typically have three sets. Venn was keen to find symmetrical figures…elegant in themselves representing higher numbers of sets and he devised a four set diagram using ellipses. He also gave a construction for Venn diagrams with any number of curves, where each successive curve is interleaved with previous curves, starting with the 3-circle diagram. It can be shown that a symmetric Venn diagram for n sets can only exist if n is prime.

Edwards' Venn diagrams
A. W. F. Edwards gave a construction to higher numbers of sets that features some symmetries. His construction is achieved by projecting the Venn diagram onto a sphere. Three sets can be easily represented by taking three hemispheres at right angles (x≥0, y≥0 and z≥0). A fourth set can be represented by taking a curve similar to the seam on a tennis ball which winds up and down around the equator. The resulting sets can then be projected back to the plane to give cogwheel diagrams with increasing numbers of teeth. These diagrams were devised while designing a stained-glass window in memoriam to Venn.


Other diagrams
Edwards' Venn diagrams are topologically equivalent to diagrams devised by Branko Grünbaum which were based around intersecting polygons with increasing numbers of sides. They are also 2-dimensional representations of hypercubes.

Smith devised similar n-set diagrams using sine curves with equations y=sin(2ix)/2i, 0≤i≤n-2.

Charles Lutwidge Dodgson (a.k.a. Lewis Carroll) devised a five set diagram.

Classroom use
Venn diagrams are used by teachers in the classroom as a mechanism to help students compare and contrast two items: characteristics are listed in each section of the diagram, with shared characteristics listed in the overlapping section.

Answer 2

Venn diagrams are a powerful way to graphically organize information.The Venn Diagram is made up of two or more overlapping circles. It is often used in mathematics to show relationships between sets. In language arts instruction, Venn Diagrams are useful for examining similarities and differences in characters, stories, poems, etc.
It is frequently used as a prewriting activity to enable students to organize thoughts or textual quotations prior to writing a compare/contrast essay. This activity enables students to organize similarities and differences visually .
in mathematics, a diagram in which sets are sensed by areas.
VENN DIAGRAMS ARE USEFUL FOR ILLUSTRATING SET OPERATIONS

Answer 3

venn diagrams, named after the
english logician john venn
(1834-1883),diagrammatically
represent the relations of
membership and inclusion and
the operations of union,
intersection,and
complementation

i hope that this helps

Answer 4

you will possibly be able to ought to state the problem clearer. i'm uncertain what the ninety 5's place is in any respect. in case you propose that the ninety 5 dislikes the two canines and cats, that would go away one 0 five who like one or the different or the two. because fifty 9 cat likers + sixty 8 dogs likers = 127 there must be some overlap. Subtract sixty 8 from one 0 five to get how lots of the one 0 five are no longer cat likers: 37. because of the fact the one 0 five the two like cats or canines or the two, and those 37 of them do unlike cats, they should like canines. That debts for 37 dogs likers and leaves fifty 9-37=22 dogs likers who additionally should love cats. 22.

Answer 5

It is surely not a diagram concernig venn-triloquists!

Answer 6

Understand what Venn Diagram is. Click on the link to Watch the VIDEO explanation:
http://bit.ly/1ISQVzi

Explanation of Venn Diagrams
As we know this is a Venn diagram. It is a visual presentation of sets. We have learnt about the union of sets and the intersection of sets. This can be diagrammatically represented by using a rectangle and circles or ellipces. The rectangle is used to represent a universal set while circle and ellipces represent the subsets of universal set.
To make this clear we consider an example. Here the universal set represents a collection of objects in a classroom, desk, bench, book, chair, duster and chalk piece. Set A contains a chalk piece, a duster and a chair. Notice that set A is a subset of the given universal set.
Set U is equal to desk, bench, book, chair, duster, chalk piece .
Set A is equal to chalk piece, duster, chair.
Now this can be represented in a Venn diagram. The rectangle represents the universal set. The circle representing the subset A contains a chalk piece, a duster and a chair while the desk, the book and the bench which are part of the universal set are all present outside the circle but inside the rectangle. Similarly we can use the Venn diagrams to represent the union and intersection of sets.
Let us consider the objects owned by two friends Mahesh and Ganesh. Mahesh has a dining table, a dressing table, a sofa set, a radio and a television represented by Set X. Ganesh has a dressing table, a radio, a cot and a computer represented by Set Y. Set X and Set Y have the dressing table and the radio in common.
Click on the Venn diagram button to view the representation of the sets in a Venn diagram.
Venn diagrams can also be used to find the cardinal number of a set. Let us consider an example and learn to find the cardinal number of a set using a Venn diagram.
A florist had 100 garlands of which 35 were garland with only jasmine flowers, 42 were garlands with only roses and the remaining garlands were a combination of both flowers. He wants to know the number of garlands that had both jasmine and rose. Shall we try to help him in finding the solution?
The number of garlands which had only jasmine is equal to 35. The number of garlands which had only rose is equal to 42. The total number of garlands is equal to 100. Therefore, the number of garlands having both rose and jasmine is equal to total number of garlands minus number garlands containing only jasmine added to the number of garlands containing only rose. That is equal to 100 minus 35 plus 42.
Therefore, the number of garlands containing both jasmine and rose is 23.
Let us consider an another example. Out of 8o students in a class 35 play cricket, 20 play football and 15 play both cricket and football. The class teacher wants to know the number of students who play neither cricket nor football. Shall we help the teacher find the number?
The total number of students in the class is equal to 80. The number of students who play cricket only is equal to the number of students who play cricket 35 minus the number of students who play both 15 that is equal to 20. Similarly the number of students who play only football is equal to the number of students who play football 20 minus the number of students play both 15 that is equal to 5. Therefore the number of students who neither play cricket nor football is equal to n of Set U minus n of C plus n of F plus n of C intersection F is equal to 80 minus 20 plus 5 plus 15 that is equal to 80 minus 40 that is equal to 40.

Answer 7

Something they taught us in Maths class 25 years ago but I have never ever ever needed in any part of my life since that day. Like algebra and Shakespeare, you'll never EVER need it and it's only taught just to bore the pants off schoolkids.

Answer 8

It's a table of logic functions to map a result of a combination of logic functions.