In a class of 70 student 40 belong to the red Cross society 27 belong to the girls guide society and 12 belong to both the red Cross society and the girls guide society. The remaining student do not belong to any of the two societies.
1. illustrate the information on a Venn diagram
First, let's label the sets. Let R represent the set of students belonging to the Red Cross society, G represent the set of students belonging to the Girls Guide society, and N represent the set of students who do not belong to either society.
From the information given, 40 students belong to the Red Cross society, 27 students belong to the Girls Guide society, and 12 students belong to both societies.
The Venn diagram representing this information is as follows:
_______________
| |
| R |
|______|____|
| |
| G |
|______|____|
N
In the diagram, the overlapping region between R and G represents the 12 students who belong to both societies. The non-overlapping regions of R and G (outside the overlap) represent the students who only belong to one of the societies.
The remaining region outside R, G, and the overlap represents the students who do not belong to either society (N).
2. Determine the number of students who do not belong to any of the two societies.
To find the number of students who do not belong to any of the two societies, we need to add up the number of students who only belong to the Red Cross society and the number of students who only belong to the Girls Guide society, and subtract the number of students who belong to both societies.
Students who only belong to the Red Cross society = Total students in R - Students in the overlap = 40 - 12 = 28.
Students who only belong to the Girls Guide society = Total students in G - Students in the overlap = 27 - 12 = 15.
Therefore, the number of students who do not belong to either society (N) = Total students - Students in R - Students in G + Students in the overlap = 70 - 40 - 27 + 12 = 15.
So, there are 15 students who do not belong to any of the two societies.
To illustrate the given information on a Venn diagram, we can create two overlapping circles. We'll label one circle "Red Cross Society" and the other circle "Girls Guide Society".
The circle representing the Red Cross Society will contain 40 students, and the circle representing the Girls Guide Society will contain 27 students.
In the overlapping section of the circles, we'll place 12 students who belong to both societies.
The remaining students who do not belong to any of the two societies will be represented outside the circles.
Here is a visual representation of the information:
Red Cross Society: 40
|
| 12
| ____⎧__________
|| ⎮
|| ⎮ 27
||____________⎪__________________
| ⎪
No Society: x (where x is the number of students who do not belong to any society)
Please note that the numbers written outside the overlapping sections are not mentioned in the question and thus cannot be determined.
To illustrate the information on a Venn diagram, we can start by drawing two overlapping circles. Let's label one circle as "Red Cross Society" and the other as "Girls Guide Society."
Inside the Red Cross Society circle, we write the number 40 to represent the total number of students belonging to that society. Inside the Girls Guide Society circle, we write the number 27 to represent the total number of students belonging to that society.
In the overlapping region of the circles, we write the number 12 to indicate the students who belong to both societies.
Finally, outside of both circles, we write the number of students who do not belong to either society.
Here is the completed Venn diagram:
________
/ \
/ \
/____ 12 ____\
\ | /
\ | /
\ /
_________
(Red Cross Society) (Girls Guide Society)
The numbers inside the circles represent the students belonging to each society, while the number in the overlapping region represents the students belonging to both societies. The area outside the circles represents the students who do not belong to either society.