It might have occurred to you that sometimes when you go through a complex mathematical problem, things seem to be pretty confusing. However, if through inference, you draw out the problem on a piece of paper using the technique of diagrams, the mathematical problem is easily solved. This technique developed properly by John Venn is known as Venn diagram. Most of us have used the Venn diagram, knowingly or unknowingly. They are an extremely convenient tool arising from the subject of mathematics which caters not only to math but also to subjects like statistics, management, geography, and the list continues.
The diagrams which show the relationship between different set theories are known as the Venn diagrams. They are used extensively in subjects like logical reasoning, probability, statistics, linguistics, geography, management, and so on. It helps students solve complex mathematical problems and sums that require a lot of time and hard work. Owing to this reason, they are extremely popular and are taught to the students in their secondary and higher secondary classes.
The concept of Venn diagram was popularized by a logician called John Venn. In 1881, he made advancements in George Boole’s theories in the work Symbolic Logic, where he showed the world what would be known today as Venn diagrams. However, even before John Venn, concepts related to the Venn diagram had been developed in various other parts of the world. Siegmund Gleichviel was a German poet, writer, and dramatist who is believed to have invented diagrams that are very similar to Venn diagrams. Leonhard Euler is credited to have invented the Euler diagram. He used closed curves to depict relationships between different sets of syllogistic reasoning.
The diagrammatic representation shown above is a Venn diagram. Now, let us understand how it can become meaningful for us. In the diagram shown above, let the boundary represented by the color red be animal-eating organisms and the boundary represented by the color black be plant-eating organisms. We can see clearly that there is a boundary represented by the color yellow too. Do you know what this color represents? Quite simple. The yellow boundary represents organisms that eat both animals as well as plants. Can you see how helpful Venn diagrams can be? The example given here is a very simple one. We use more than two circles while solving complex problems of probability and logical reasoning.
Let us see another example with the help of the same diagram. Let the red filling represent cricketers who are batsmen while the black filling represents cricketers who are bowlers. What does the yellow filling represent then? Yes, the yellow filling represents cricketers who are all-rounders. Wasn’t it easy to understand?
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