Profile
Settings
Refer your friends
Sign out
Introduction
A Venn diagram, popularised by John Venn during the early 1800s, is a broadly used chart style that depicts the logical connection among pairs. The diagrams have been used in likelihood, reasoning, statistical data, linguistics, as well as computer programming to teach high school set theory and also to highlight simple set connections. To depict sets, a Venn diagram utilizes simple confined curves traced on a surface. These shapes are frequently ellipses or curves or circles.
Before Venn, similar approaches had already been suggested. They were proposed in 1768 by Leonhard Euler and in 1712 by Christian Weise. Venn popularised the concept in his 1881 book Symbolic Logic.
What is a Venn Diagram?
A logical diagram or a set diagram is another name for a Venn diagram. It’s a diagram that depicts all logical connections among a finite variety of different sets. A Venn diagram is a graphical representation that utilizes circles to depict relationships between objects or limited groups of objects. Circles that intersect share characteristics, whereas circles that do not intersect do not share. Elements are represented as coordinates in the surfaces and planes, and sets are represented as regions within closed contours in such graphs. A Venn diagram is made up of superimposing closed curvatures, generally circles, that each portrays a set of data.
They’ve long been recognized as valuable educational resources. Venn diagrams are being used as a portion of the beginner’s logic syllabus and in primary school educational objectives all over the globe ever since the mid-1950s.
How to understand Venn Diagram
To understand a Venn diagram, we have to understand the chart of it. For instance, let us take the example of a School. Where some students are from maths, some from science and some from commerce. If we represent It is a Venn chart it will be as.
If we understand this Venn diagram it depicts that there are three sets of students, one set from science, one from commerce, and one from maths. So, we can see that there is a commonplace containing 10 students. Since that portion is an intersection of all the three circles, we can say that all the 10 students have maths, science, and commerce as their subjects.
And the portion containing 20 and 30 as the number of students depict that those students have two subjects in common. As portion with 30 students has maths and science in common, 20 students have maths and commerce in common and another 20 students have both science and commerce in common.
And the rest portion which is not in the territory of any set tells the number of students in that particular subject itself. As portion with several students 80 says that those 80 students have only maths subject, 90 students have only science as their subject and 60 students have only commerce as the subject.
If anyone asks that total how many students study commerce subject, then we have to tell the number of students that have only commerce or commerce with some other subjects as here in this example. We can see that 110 students study commerce i.e., 60+20+20+10. Or simply we call to understand it as the total number of values in the particular set as here a total number of students in the set of commerce.
Applications
Venn diagrams are being utilized to model how elements connect in the context of a larger context, such as a universe, data set, or environment. For instance, a Venn diagram can also be used to find similar firms in the same sector by showing the items that both businesses sell (wherever circles overlap) as well as the goods that are unique to the firm (outer circles). Venn diagrams represent simply graphical representations of such relationship that occurs between two groups of items at their most fundamental level. They can, however, be much more complicated. Despite this, the Venn diagram’s simplified intention of illustrating concepts and collectives has led to its widespread use in a variety of fields, such as numbers, language teaching, reasoning, schooling, computer programming, and industry.
Venn diagram questions with examples
Let us now see some common Venn diagram questions with the help of the Venn diagram example.
Consider a class of cars manufactured by various companies manufacturing SUVs, Trucks, and Sports. The information may not be correct and data is taken for only understanding the concept.
So let us see how many questions can arise from the above chart.
The first question we can get is how many car manufacturing companies manufacture only SUVs? The answer to this question is as we can see in the circle of SUVs the number of car companies listed does not overlap with the circles of any other car. As we can see only TATA, Honda, Audi, and KIA manufacture SUVs.
Another question that can arise is, which company produces all the three kinds of cars. We can simply see the portion that is an intersection of all the three circles and the value in it. Here, Ford produces cars of all three kinds.
Another question is that Toyota manufactures which kind of vehicles. Again, we can have a look at the place where Toyota is placed. We can see Toyota is at the intersection of trucks and sports. So, it produces both trucks and sports vehicles.
Similarly, there can be many questions arising from the topic of the Venn diagram in preliminary classes, competitive exams, higher studies, psychological exams, etc.
Conclusion
To sum up, a Venn diagram is a graphical representation, that represents all the logical connections that can be set between two or more sets of data. This concept was developed by Jon Venn in the early 1800s. Ven diagrams are used in various places, in schools to teach students, in industries to train employees, in competitive exams, and other places too.
Table Of Contents
- What Is Binary Logic?
- Assumptions In Binary Logic
- Binary Logic Questions Types
- Solved Examples
- FAQs
- Conclusion
- Reference
What Is Binary Logic?
In binary logic questions, people either say something true or something wrong. There are three types of people in this group:
- Truth-teller: A truth-teller is supposed to speak the truth always. Every statement made by a truth-teller is always true.
- Liar: A liar is supposed to speak the lies always. Every statement made by a liar always is false.
- Alternator An alternator person alternates between telling the truth and lying. If this person’s initial assertion is correct, the second will be incorrect, the third will be correct, and so on. Similarly, if this person’s first statement is false, the second will be true, the third will be false, and so on. This person makes no specific amount of truthful or false assertions, but the order is always FALSE-TRUE-FALSE or TRUE-FALSE-TRUE.
It’s all about making certain assumptions in binary logic questions (kind of assumptions are described later). These assumptions may result in certain inconsistencies, which are evidence that our assumptions are incorrect. If we don’t obtain a single contradiction for any assumption, we’ve found the answer to the provided binary logic problem.
A collection of principles for dealing with statements that must be true or false is known as binary logic. All binary logic systems have three operations in common: AND, OR, and NOT. Many logic systems also have the procedures IF AND ONLY IF, IF….. THEN, and EOR. Because notations differ so much, it’s critical to be consistent when writing out binary logic.
Assumptions In Binary Logic
It’s all about making certain assumptions in binary logic questions.
These assumptions may result in certain inconsistencies, which are evidence that our assumptions are incorrect.
If we don’t obtain a single contradiction for any assumption, we’ve found the answer to the provided binary logic problem.
Binary Logic Questions Types
Binary Logic Questions will have people who will make statements. The overall pattern is for each of them to make three statements. The number of people can vary from 3 to 5, but if we go by the trend of the CAT exam; only 3 people’s problems have been asked in previous years.
The question will now specify how many of them are a truth-teller, a liar, or an alternator. We don’t always have someone who fits into each group.
In some circumstances, all three can be alternators, two alternators or one truth-teller, and so on. When the number of people is increased to four or five, the problem becomes even more intricate, requiring more iterations. Though CAT hasn’t introduced any four to five people problems.
Solved Questions
Question 1. Three persons A, B, and C gave these statements:
A: – either Green Party or Freedom Party won the elections.
B: – Freedom Party won the elections.
C: – neither Green Party nor Freedom Party won the elections.
Of all these three persons A, B, and C, only one of them is wrong.
Who won the elections?
Answer: Because only one individual is incorrect, the other two are stating the truth. Assuming the Freedom Party won the election. As a result, A and B’s statements are true because they satisfy our criterion that the two of them are truth-tellers. As a result, the Freedom Party triumphs in the election.
If you think the Green Party won the election, propositions B and C become untrue, and the provided condition is violated.
Question 2. Tolu, Molu, and Golu were caught by police yesterday after one of them was suspected of robbing a local bank. Following extensive questioning, the three suspects made the following statements:
Tolu: – I’m not guilty.
Molu: – I’m not guilty.
Golu: – Molu is the one who is to blame.
If just one of the three claims is true, who among the three robbed the bank?
Answer: Let’s suppose that Molu is the thief. As a result, we can observe that Tolu’s remark is correct. However, Molu’s statement is incorrect. Golu’s allegation is also valid because he is pointing to Molu as the robber. As a result, the two statements are true, indicating a violation of the provided condition.
Assume that Tolu is the thief. The remaining two statements, except for Molu’s, are now false. Tolu, then, is the thief.
Conclusion
Binary Logic is one of the most important topics in the reasoning section of the CAT exam. Binary logic has the advantage of providing a set of formal rules that may be used to check for inconsistencies in statements (propositions). Two problems based on Binary Logic should be found among the 10 questions in Logical Reasoning. The use of this logic is more in determining whether or not the statements presented are true. It allows for neither true nor untrue claims, as well as statements with varying degrees of truthfulness.
