Set theory is an important tool that allows people to group things. Students have to work with a large amount of data in Mathematics. Set theory is the basic way to keep these data in different parts. You can draw a circle and assign certain elements to it. These circles or diagrams have a common name which is called the Venn diagram. To show the data that are present in both circles, you have to overlap them. When you write the elements in the overlapped section, you will depict that those are common. The remaining that are present outside belong to the universal set.
The Working of the Diagrams
The function of these diagrams is to show the relation between the sets. If you take a small portion of a set and form a different group, they will have a connection. You can use Venn diagrams to represent super and subsets as well. Even the complement and difference of sets are possible in these diagrams. There is a rectangle that represents all the data present. Inside them, you have to form circles with the name of the sets. If none of them intersects the viewer will understand that they have no relation. In case you want them to understand clearly you can shade the portions as well.
How to Depict Different Functions?
The universal set is the basic way to start these problems. You will see in the question that there are many elements. Draw a rectangle and write the alphabet ‘U’ on the top right corner. After that draw different circles according to the number of ‘sets’ present in the question. Next, you have to see the symbols of the equations that you have to show. Whether it is a union or a compliment, the student has to solve it step by step.
Union: For this, you have to shade the entire set or the circles present in the rectangle. Suppose there are two circles A and B that you need to depict. If you want the union of them you need to shade both of them. You cannot leave a single portion without shading.
Intersection: This is the region that will allow highlighting of common data elements. There may be cases where there are the same elements present in two circles. In such situations, you have to draw them in such a way that they overlap each other. After that, shade the middle portion that is common to both circles.
Compliment: It is a special function that students can use in set theory. With this, you get to highlight portions that do not belong to the set. It becomes clear when you see the regions that do not fall in a set. For that, you have to highlight the entire portion except for that set itself. It allows the students to solve complex numerical problems when it comes to set theory. There may be questions where you have to see the Venn diagrams and tell which elements belong to the compliment section.
How can these Diagrams help in Mathematics?
It becomes much simpler when you visualize the data instead of learning. You cannot remember and calculate everything. This chapter applies to all other subjects involving complex numerical data. When you have to decide between two sets of choices, use these diagrams. Put down the data in each set and find which one suits your requirements. If one knows how to use Venn diagrams then they can detect data patterns.
It takes a lot of practice to draw and solve numerical problems with these diagrams. For better guidance, you can approach the online math classes from Cuemath.