Using Venn diagram ,in class of 50 students,17 are not intelligent ,15 are hardworking ,and 11 are neither hardworking nor intelligent .a student will pass if and only the student is both intelligent and hardworking .how many of this class will fail?
To solve this problem using a Venn diagram, we will need to represent three categories: "intelligent," "hardworking," and "neither hardworking nor intelligent."
Let's start by drawing a rectangle to represent the total class of 50 students.
[Rectangle representing the total class]
Now, let's place the information given in the Venn diagram.
Given:
- 17 students are not intelligent.
- 15 students are hardworking.
- 11 students are neither hardworking nor intelligent.
Let's start with the "neither hardworking nor intelligent" category. Place 11 in the corresponding region of the Venn diagram.
[Diagram with 11 in the "neither hardworking nor intelligent" region]
We can now fill in the remaining information. Since there are 17 students who are not intelligent, we subtract 11 from that to find that 6 students are not intelligent but are hardworking.
[Diagram with 11 in the "neither hardworking nor intelligent" region and 6 in the "hardworking but not intelligent" region]
Next, we place the 15 students in the "hardworking" region.
[Diagram with 11 in the "neither hardworking nor intelligent" region, 6 in the "hardworking but not intelligent" region, and 15 in the "hardworking" region]
Finally, we must calculate the number of students who are both intelligent and hardworking. To do this, we subtract the total number of students who are not intelligent (17) from the number of students who are hardworking (15):
15 - 6 = 9
So, 9 students are both intelligent and hardworking.
[Diagram with 11 in the "neither hardworking nor intelligent" region, 6 in the "hardworking but not intelligent" region, 15 in the "hardworking" region, and 9 in the "intelligent and hardworking" region]
To find the number of students who will fail, we add the students who are not intelligent (17) to the students who are hardworking but not intelligent (6). So, a total of 17 + 6 = 23 students will fail.
Therefore, 23 students in this class will fail.