There are various branches of mathematics such as geometry, trigonometry, algebra etc that are meant to deal with a specific type of problems. Set Theory is one of the branches of mathematics that deal with the problems related to sets. A set is collection of entities such as people, numbers, objects etc that satisfy a common property that defines the set. Two or more sets may or may not share a common a specific set of entities. The sets which have certain elements in common are termed as intersecting sets and the elements lying in both the sets are called as common elements. Problems related to sets, especially intersecting sets can be easily and quickly solved with the help of a Venn diagram.
What Is a Venn diagram in Math
The first thing that you would want to know is that what is a Venn diagram in Math? A Venn diagram is a graphical representation of sets in the form of closed figures (usually circles) inside a rectangle representing the Universal Set. A Venn diagram is drawn on a plane such as a piece of paper or drawing sheet. The elements contained in a set are marked within the closed boundaries of the respective set. A Venn diagram is the simplest way to depict logical interconnections between two or more sets.
A universal set is a group of all possible elements that exist in the universe. All sets irrespective of their properties or elements forms a subset of the universal set. Thus, all the sets lie inside the rectangular boundaries of the universal set as its subset.
Now that you understand what is a Venn diagram in Math, let us try to understand more about the structure of a Venn diagram. If there are two sets A and B such that set A is a subset of set B, then set A will be represented by a small circle within larger circle representing set B. A set A is termed as a subset of another set B if all the elements of set B are part of the set A. However, all the elements of the set A need not be present in the set B.
An element is marked only once within a Venn diagram, irrespective of its occurrence in multiple sets. Two or more intersecting sets are represented by intersecting circles with some part of the circles that is common among the intersecting circles. The elements which are common to say two sets are necessarily placed in the common region of the two circles.
When there are more than two intersecting sets represented by intersecting circles for each set, there are two types of shared regions. One that is shared only between two circles and is meant for placing that are common in only those two sets. Another shared region is that which is present in all the circles. This is where are we put those elements that are part of all the sets.
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