Venn Diagram for Students Wearing Red Shirt, Blue Pants and Black Shoes

This article explains how to create a Venn diagram for students wearing red shirt, blue pants and black shoes using set theory and intersection of sets. It includes solved examples and computations to help understand the concept better.

Mathematics
STUDENT Id /name
[Pick the date]

Let event A highlight the number of students wearing red shirt
Let event B highlight the number of students wearing blue pants
Let event C highlight the number of students wearing black shoes
The following data has been provided to facilitate creation of the Venn Diagram for the given
situation.
N(A) = 8 (i.e. number of elements belonging to set A is 8)
N(B) = 24
N(C) = 10
N(A∩B∩C) = 3
N(A∩B) = 4
N(B∩C) = 7
N(A∩C) = 5
Based on the given information, the following computation may be performed.
N(A∩B∩C’) = N(A∩B) - N(A∩B∩C) = 4-3 = 1
N(B∩C∩A’) = N(B∩C) - N(A∩B∩C) = 7-3 = 4
N(A∩C∩B’) = N(A∩C) - N(A∩B∩C) = 5-3 = 2
N(A∩B’∩C’) = N(A) - N(A∩B∩C’) - N(A∩C∩B’) - N(A∩B∩C) = 8 – 1-2-3 = 2
N(B∩C’∩A’) = N(B) - - N(A∩B∩C’)- N(B∩C∩A’) - N(A∩B∩C) = 24-1-4-3 = 16
N(C∩A’∩B’) = N(C) - - N(B∩C∩A’) - N(A∩C∩B’) - N(A∩B∩C) = 10-4-2-3= 1
Also, since the total number of students is 30, hence the sum of all the elements in the Venn
diagram should 30.
Hence, N(A∩B’∩C’) + N(B∩C’∩A’) + N(C∩A’∩B’) + N(A∩B∩C’) + N(B∩C∩A’) +
N(A∩C∩B’) + N(A∩B∩C) + N(A’∩B’∩C’) = 30
2+16+1+1+4+2+3 + N(A’∩B’∩C’) = 30

Hence, N(A’∩B’∩C’) = 30 – (2+16+1+1+4+2+3) = 1
Based on the above computations the Venn Diagram is shown below.
 Orange denotes the number of students wearing red shirt and blue pants but not black
shoes
 Green denotes the number of students wearing red shirt and black shoes but not blue
pants
 Blue denotes the number of students wearing blue pants and black shoes but not red shirts
 Yellow denotes the number of students wearing red shirt and blue pants and black shoes
 n=1 refers to the student who does not wear red shirt or blue pants or black shoes.