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Hi All,
I have recently uploaded a video on YouTube to discuss Overlapping Sets (2 Variables) in Detail:
Following is covered in the video
ยค Table Method - Theory and Example ยค Venn Diagram - Theory and Example
Table Method - Theory
Let's understand the theory using an example:
Some students in the class have taken Maths, some have taken English and we need to find how many have taken both, only maths, only English, neither of them, etcโฆ
We will draw a 2x2 grid/table to solve this (As shown below)
Attachment:
table-1.jpg [ 9.17 KiB | Viewed 851 times ]
Now, following is the notation in the table:
EM -> Students who have taken Both the subjects E๐ย ฬ -> Students who have taken ONLY English ๐ย ฬ M -> Students who have taken ONLY Maths ๐ย ฬ ๐ย ฬ -> Students who have taken NEITHER E -> Total students who have taken English ๐ย ฬ -> Total students who have NOT taken English M -> Total Students who have taken Maths ๐ย ฬ -> Total students who have NOT taken Maths T -> Total students
Now, given the values in the questions we will use a combination of following equations to solve the problem E = EM + E๐ย ฬ ๐ย ฬ = ๐ย ฬ M + ๐ย ฬ ๐ย ฬ M = EM + ๐ย ฬ M ๐ย ฬ = E๐ย ฬ + ๐ย ฬ ๐ย ฬ E + ๐ย ฬ = M + ๐ย ฬ = T EM + E๐ย ฬ + ๐ย ฬ M + ๐ย ฬ ๐ย ฬ = T
Table Method - Example
Q1. Out of the 40 students in a class, 10 are in Drama club, 35 are in Swimming club and 8 are in both. Find out the number of students who are in neither of them.
Some students in the class have taken Maths, some have taken English and we need to find how many have taken both, only maths, only English, neither of them, etcโฆ
We will draw a Venn Diagram to solve this (As shown below)
Attachment:
venn-1.jpg [ 19.09 KiB | Viewed 846 times ]
Now, following is the notation in the table:
EM -> Vertical black line portion, Students who have taken Both the subjects E๐ย ฬ -> Horizontal Blue lines, Students who have taken ONLY English ๐ย ฬ M -> Horizontal Red lines, Students who have taken ONLY Maths ๐ย ฬ ๐ย ฬ -> Horizontal Yellow lines, Students who have taken NEITHER E -> Blue Circle, Total students who have taken English ๐ย ฬ -> Anything outside the blue circle but inside rectangle, Total students who have NOT taken English M -> Red Circle, Total Students who have taken Maths ๐ย ฬ -> Anything outside the red circle but inside rectangle, Total students who have NOT taken Maths T -> Rectangle
Now, given the values in the questions we will use a combination of following equations to solve the problem E = EM + E๐ย ฬ ๐ย ฬ = ๐ย ฬ M + ๐ย ฬ ๐ย ฬ M = EM + ๐ย ฬ M ๐ย ฬ = E๐ย ฬ + ๐ย ฬ ๐ย ฬ E + ๐ย ฬ = M + ๐ย ฬ = T EM + E๐ย ฬ + ๐ย ฬ M + ๐ย ฬ ๐ย ฬ = T
Venn Diagram - Example
Q2. Out of the 40 students in a class, 10 are in Drama club, 35 are in Swimming club and 8 are in both. Find out the number of students who are in neither of them. (Same as above)