Venn Diagram Math

The relationship between two or three sets can be shown diagrammatically in the form of circles called the Venn-diagram. They were first given by the mathematician John Venn and hence the name for the diagrams. As we know set is the collection of unique things which are called the elements of the set. Consider the following Venn Diagram examples, List of odd numbers less than 15 forms a set which can be denoted as set A={1,3,5,7,9,11,13} here each element is unique.

Let us now learn how to draw Venn-diagrams to show the relationship between two sets. Let set A={1,3,5,7,9,11}, a set of odd numbers and set B={1,2,3,5,7,11} set of prime numbers.
The Venn-diagram of these two sets would be as given below,

In the above diagram the two circles represent each set, set A and set B. Both the circles with all the numbers represent ‘Union of sets’.

The green shaded region represents the numbers in both the sets, this is called the ‘Intersection of sets’, the yellow region represents only A, that is the element present in only set A and the orange region represents the element present in only set B.

Thus one glance at the Venn-diagram gives all the possible information which gives a logical relationship between the sets. At times we see Venn diagram lines, these lines are provided to write the elements or at times lines are used to show the relationship between the sets using line shading.

Venn diagram can also be used to show the relationship between three sets which would be a three circle Venn diagram.

For example: In a group of 23 students, 12 read mathematics, 15 read statistics and 11 read Physics, 4 read Mathematics only, 7 read Statistics only, 3 read Physics only, 4 read all the three subjects, 1 reads only Math and Statistics not Physics, 3 read only Mathematics and Physics not Statistics and 3 read only Statistics and Physics not Mathematics. Let us now write down all the given data to draw the 3 circle Venn diagram.

The total number of students is denoted using the symbol ‘µ’ which is ‘mu’, n(MUPUS)= µ=23, Mathematics =n(M), Physics=n(P) and Statistics=n(S). Intersection is shown with a symbol ‘∩ ‘showing the elements common to both the sets.

Elements not present in a set is shown by compliment, not A is A’. n(M)=12, n(P)=11 and n(S)=15. n(M∩P∩S)=4 and hence, n(M∩P)=7, n(P∩S)=7 and n(M∩S)=5. In the Venn-diagram below each color represents a logical relationship,