In a class of 80 students,53 study Biology,36 study Art and Biology,34 study Art and Chemistry, 6 study Biology only and 18 study Biology but not Chemistry. Illustrate the information in a Venn diagram. Determine the number of students who study:Art only and Chemistry
Well, it seems like we're in for a Venn-tastic time! Let's put on our artistic hats and draw a Venn diagram to illustrate the information.
First, we'll draw three overlapping circles to represent Biology, Art, and Chemistry. In the overlapping areas, we'll write down the number of students studying both subjects.
Now, let's fill in the numbers. We know that 53 students study Biology, so we'll write that number in the circle representing Biology. Similarly, 36 students study Art and Biology, so we'll write that number in the overlapping area between Biology and Art.
Next, 34 students study Art and Chemistry, so we'll write that number in the overlapping area between Art and Chemistry. We also know that 6 students study Biology only, so we'll write that number in the Biology circle, outside of any overlapping areas. Lastly, 18 students study Biology but not Chemistry, so we'll write that number in the Biology circle, away from the overlapping area with Chemistry.
Now, let's figure out the number of students who study Art only and Chemistry. To do that, we need to add up the students who study Art and Biology (36), students who study Art and Chemistry (34), and students who study only Art and not Biology or Chemistry. Since we don't have that specific number, we'll have to calculate it based on the information available.
We know that 53 students study Biology, and 36 study Art and Biology. So, to find the number of students studying only Art, we subtract the number of students studying Art and Biology from the total number of students studying Art:
Students studying only Art = Total students studying Art - Students studying Art and Biology
Students studying only Art = 36 - 34
Students studying only Art = 2
Now, to find the number of students studying Art only and Chemistry, we'll subtract the number of students studying only Art from the total number of students studying Art and Chemistry:
Students studying Art only and Chemistry = Total students studying Art and Chemistry - Students studying only Art
Students studying Art only and Chemistry = 34 - 2
Students studying Art only and Chemistry = 32
Therefore, the number of students who study Art only and Chemistry is 32.
To determine the number of students who study Art only and Chemistry, we need to use the information provided and create a Venn diagram.
Step 1: Draw a rectangle to represent the entire class. Label it as "Students".
Step 2: Inside the rectangle, draw two overlapping circles. Label one as "Biology" and the other as "Art and Chemistry".
Step 3: We know that 53 students study Biology, so write "53" inside the Biology circle.
Step 4: We also know that 36 students study both Art and Biology, so write "36" in the overlap of the Biology and Art circles.
Step 5: Similarly, 34 students study both Art and Chemistry, so write "34" in the overlap of the Art and Chemistry circles.
Step 6: We know that 6 students study Biology only, so write "6" in the non-overlapping part of the Biology circle.
Step 7: Lastly, we know that 18 students study Biology but not Chemistry, so write "18" in the non-overlapping part of the Biology circle that does not intersect with the Art circle.
Now, let's calculate the number of students who study Art only and Chemistry:
To find the number of students who study Art only, we need to subtract the following from the total number of students who study Art:
1. The number of students who study both Art and Biology (36)
2. The number of students who study both Art and Chemistry (34)
Therefore, the number of students who study Art only is 36 + 34 = 70.
However, we need to exclude the students who also study Biology, meaning we need to exclude the overlapping part of the Biology and Art circles. So subtract the number of students who study both Art and Biology (36) from the previous result:
70 - 36 = 34.
Therefore, 34 students study Art only and Chemistry.
To determine the number of students who study Art only and Chemistry, we need to subtract the number of students who study both Art and Chemistry from the number of students who study Art.
Given information:
- Total students: 80
- Students who study Biology: 53
- Students who study Art: 36
- Students who study Art and Biology: 36
- Students who study Art and Chemistry: 34
- Students who study Biology only: 6
- Students who study Biology but not Chemistry: 18
To create a Venn diagram, we can start by drawing two overlapping circles. Label one circle as "Biology" and the other as "Art." The intersection between these two circles will represent students who study both Biology and Art.
Now let's fill in the numbers we have:
- Students who study Biology only: 6 (fill this number in the "Biology" circle but not in the intersection)
- Students who study Biology but not Chemistry: 18 (fill this number in the "Biology" circle but not in the intersection)
- Students who study Art and Chemistry: 34 (fill this number in the intersection)
- Students who study Art and Biology: 36 (fill this number in the intersection)
Since the total number of students is 80, we can find the number of students who study Art only by subtracting the numbers we have already used:
Students who study Art only = Total students - (Students who study Biology only + Students who study Biology but not Chemistry + Students who study Art and Biology + Students who study Art and Chemistry)
Students who study Art only = 80 - (6 + 18 + 36 + 34)
Students who study Art only = 80 - 94
Students who study Art only = -14 (This means that there is an error in the given information, as it is not possible to have negative students. Please check the provided information again.)