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express in set

Venn diagrams are particularly useful for showing relationships between units, as we will see within the examples below. First, we will use a Venn diagram to search out the intersection of two units.The intersection of two sets is all the elements they’ve in frequent. The Venn diagrams on two and three units are illustrated above.

There can be many questions formed on these kinds of sets. But you can easily solve them using little manipulation and basic addition and subtraction. With a little practice, you can easily and quickly solve questions of sets either using Venn diagrams. A universal set is the set of all possible elements that can be used in a given context. The elements within the universal set are unique and not repeated.

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As it includes every item, we can refer to it as ‘ the universal Set’. It means that every other Set that is drawn inside the rectangle represents the Universal Set. Venn Diagrams are used in mathematics to divide all possible number types into groups. Venn Diagrams are used in different fields such as linguistics, business, statistics, logic, mathematics, teaching, computer science etc.

Euler diagrams include only the actually attainable zones in a given context. In Venn diagrams, a shaded zone could characterize an empty zone, whereas in an Euler diagram the corresponding zone is missing from the diagram. For instance, if one set represents dairy merchandise and another cheeses, the Venn diagram incorporates a zone for cheeses that aren’t dairy products.

Drawing Venn Diagram

A Venn diagram consists of multiple overlapping closed curves, often circles, each representing a set. The factors inside a curve labelled S symbolize parts of the set S, while factors exterior the boundary symbolize parts not in the set S. The Venn diagram template has a rectangle inside which two or more circles are drawn.

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A Logical Reasoning & Data Interpretation contains 30% weightage in CAT exams. A Venn diagram is a diagram that reveals all attainable logical relations between a finite assortment of various units. The points inside a curve labelled S represent components of the set S, whereas points exterior the boundary characterize elements not in the set S. Scientific Research is another area in which Venn Diagrams are heavily used. A lot of scientific research is generally concerned with answering questions related to scientific phenomena, concepts, and theories.

Cardinality of a Set means the number of elements in the set. Complement of a set contains elements that are NOT in the original set. In Venn diagrams the curves are overlapped in each potential way, showing all attainable relations between the units. They are thus a particular case of Euler diagrams, which do not necessarily present all relations. Of course, the objects being studied in skilled diagrams are often not candy bars or movie characters. And there’s much more you need to perceive to use them successfully.

Universal Set: Important Points

The Above Venn Diagram is A U B when neither A is a subset of B or B is a subset of A. Union of Sets using Venn Diagrams in different cases like Disjoint Sets, A ⊂ B or B ⊂ A, neither subset of A or B is explained in the below figures. The Following Venn Diagrams show the Relationship between Sets. The Relation between them is explained with a description below the diagram. Now 2, 3 and 7 are the only elements of U which do not belong to A. Symbolically, we write A′ to denote the complement of A with respect to U.

An example of an infinite universal set is the set of natural numbers, which is represented as . The ellipsis mark (…) signifies that the set continues without an end. The union of two sets can be represented by a Venn diagram as shown in following figure. If there are no common elements between two sets, it means they are Disjoint sets.

Let’s have a synopsis of the uses of Set Theory and its Applications in Problems. If at all A is a finite set then the number of elements in Set A is given by n. The above diagram depicts the relationship between sets when neither A ⊂ B nor B ⊂ A. Learn about the difference of sets in various cases like A – B when neither A ⊂ B nor B ⊂ A, when A and B are disjoint Sets in the below modules.

Complement of a set denotes the elements that do not belong to the set. For example Complement of Set A is anything present in the Universe but not in Set A. The cardinality of the union of sets is the sum of the cardinalities of the individual sets, minus the cardinality of their intersection.

The number of circles may vary, but the more the number of circles, the more complex the diagram is to understand. Now that we know the definition and symbol of the Venn diagrams, moving forward lets us understand how we can draw them. There are no particular symbols for Venn diagrams, the symbols are basically for the operations involved.


Disjoint units are at all times represented by separate circles. A simple Venn diagram definition would be, a graphic representation of concepts and their relationships using circles. It is known in different names like Set Diagrams and Logic Diagrams. Children start learning the usage of Venn diagrams as early as elementary grades. Set theory is an individual branch of learning in mathematics.

In particular, Venn Diagrams are used to show De Morgan’s Laws. Venn diagrams are additionally useful in illustrating relationships in statistics, probability, logic, and more. So, in the music and science class example, the intersection is indicated in grey and means that Tyler and Leo are in each your music and science classes.


Using Venn diagrams permits kids to sort data into two or three circles which overlap in the center. You indicate parts in a set by putting brackets round them. F. Edwards, Branko Grünbaum, Charles Lutwidge Dodgson (a.k.a. Lewis Carroll) developed extended implications of Venn diagrams.

Let us understand the major symbols applied in a Venn diagram. Firstly, set the background information of your study ready. Visual representations are significant in retaining and achieving a better understanding of a content.

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When two sets are brought together to analyze their relationships, it is called the Union of Sets . When the aspects of the two concepts overlap, it is called the Intersection of Sets . These are the most common terms one may come across while applying Venn Diagrams. They show all of the attainable mathematical or logical relationships between units . Such logical diagrams, in addition to making the data look well presented, also allow you to understand the information very easily.

Union of Sets is different from Universal Set as it includes all elements belonging to either set or both. The universal set of all possible outcomes in rolling a six-sided die is . The set of all possible elements that can be used in a given context. Universal Set is represented by arectangle in Venn Diagrams. The Empty Set is recognized as the complement of the Universal Set.

Union of two sets contains any elements that are in the first set OR in the second set. Intersection of two sets contains only elements that are in BOTH sets . The sets \(\left( \right)\) , \(\left( \right)\) and \(\left( \right)\) are mutually disjoint sets. Express in set notation the subset shaded in the Venn diagram. CAT Venn Diagram is important and useful in logical as well as quant section. As Logical reasoning section contain a total of 20 questions and out of that few questions are from Venn Diagram .

In CAT and other MBA entrance exams, questions asked from this topic involve 2 or 3 variable only. Therefore, in this article we are going to discuss problems related to 2 and 3 variables. Let’s take a look at some basic formulas for Venn diagrams of two and three elements. Additionally, they suggest to deal with singular statements as statements about set membership.

They are a part of the curriculum at school where kids learn different Venn Diagram formulas to derive solutions. Data patterns can be identified through Venn diagrams which are helpful in learning probabilities and correlations. Sets are defined as well-organized collections of elements in Maths. Intersection Operation between Three Sets A, B, C is given above. The Shaded Region includes the elements that are in Sets A, B, C. Intersection of Sets using Venn Diagrams in different cases like Disjoint Sets, A ⊂ B or B ⊂ A, neither subset of A or B is explained in the below figures.

These are widely used in set theory, logical reasoning, mathematics, industries to present their assets, in the teaching sector, statistics and so on. In this heading, you will learn about the Venn diagram in sets with some most commonly used operations. These diagrams consist of rectangles and closed curves usually circles. The universal set is represented by rectangle and its subsets by circles. The overlapping region or intersection would then represent the set of all wooden tables. Shapes aside from circles can be employed as shown beneath by Venn’s personal higher set diagrams.

The shaded portion in Figure indicates the intersection of A and B. Find the number of students who like watching at least two of the given games. Find the number of students who like watching only one of the three given games. Find the ratio of the number of students who like watching only football to those who like watching only hockey. In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basketball both.


These diagrams depict components as factors in the aircraft, and sets as areas inside closed curves. The drawing is an example of a Venn diagram that shows the relationship among three overlapping units X, Y, and Z. The intersection relation is defined as the equal of the logic AND. The intersection of three Sets X, Y, and Z is the group of elements that are included in all the three Sets X, Y, and Z. Let us understand the Venn Diagram for 3 Sets with an example below. A Venn Diagram is a diagram that is used to represent all the possible relations of different Sets.

Simple venn diagram symbols diagrams are used in the classroom to show college students logical group of their thoughts. A universal Set is defined as a set that incorporates all the elements or objects of other Sets including its elements. N in the above Venn Diagram formula represents the Number of elements in Set X.

Although Venn Diagrams are commonly used to represent intersection, union, and complements of Sets, they can also be used to represent subsets. Consider two sets, P and Q, then the intersection of P and Q contains all the common elements that belong to set P and Q. These diagrams in general have circles enclosed within a rectangle box. The circles may be overlapping, intersecting or non-intersecting depending on the relationships within the given data set.