In a class of 40 students, 22 study Art, 18 study Biology, 6 study only Chemistry. 5 study all the three subjects. 9 study Art and Biology, 7 study Art but not Chemistry. 11 study exactly one subject. Illustrate this o a venn diagram.
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Well, let's imagine this Venn diagram as a circus! We have three main rings: Art, Biology, and Chemistry. In the center, we'll have our amazing performers who study all three subjects, balancing on a unicycle and juggling at the same time!
In the Art ring, we have 22 students, and 9 of them are also studying Biology, so we draw a little overlap between the Art and Biology rings. But wait, 7 students are studying Art but NOT Chemistry, so we shade a portion of the Art ring without overlapping with any other ring.
Next, we move to the Biology ring. We know that 18 students study Biology, and 9 of them already overlap with Art. Additionally, 5 of these students are also taking Chemistry, so we have another overlap, this time between Biology and Chemistry.
Finally, we turn to the Chemistry ring. We are informed that 6 students study Chemistry alone. Since 5 students are already juggling between all three subjects, we shade the remaining single Chemistry student in the ring.
At last, we have our wonderful Venn diagram circus, with the three rings representing Art, Biology, and Chemistry, along with the overlapping areas showcasing the connections between these subjects. Enjoy the show!
To illustrate this information on a Venn diagram, we need to consider the three subjects: Art, Biology, and Chemistry. Let's go step by step to build the diagram.
Step 1: Draw three overlapping circles to represent the three subjects: Art, Biology, and Chemistry. Make sure the circles overlap in the middle.
Step 2: We are given that 5 students study all three subjects. Place the number 5 in the region where all three circles overlap.
Step 3: We know that 9 students study Art and Biology. Place this number in the overlapping region of the Art and Biology circles outside the region of all three subjects.
Step 4: We are told that 7 students study Art but not Chemistry. Place this number in the overlapping region of the Art and Biology circles that does not overlap with the Chemistry circle.
Step 5: We know that 6 students study only Chemistry. Place this number in the region of the Chemistry circle that does not overlap with any other circle.
Step 6: We are given that 11 students study exactly one subject. To find how many study only Art, only Biology, or only Chemistry, we will need to do some calculations.
To calculate the number of students studying only Art, we start with the total number of students studying Art (22) and subtract the number in the overlapping region with Biology (9) and the overlapping region with all three subjects (5). So, 22 - 9 - 5 = 8 students study only Art. Place this number in the region of the Art circle that does not overlap with any other circle.
Similarly, to calculate the number of students studying only Biology, we start with the total number of students studying Biology (18) and subtract the number in the overlapping region with Art (9) and the overlapping region with all three subjects (5). So, 18 - 9 - 5 = 4 students study only Biology. Place this number in the region of the Biology circle that does not overlap with any other circle.
To calculate the number of students studying only Chemistry, we start with the number of students studying only Chemistry (6). Place this number in the region of the Chemistry circle that does not overlap with any other circle.
Step 7: Finally, we can find the number of students who do not study any of the three subjects by adding up all the numbers outside the overlapping regions of the circles.
In summary, the Venn diagram would have the following numbers in the respective regions:
Art: 8 (only Art), 7 (Art but not Chemistry), 5 (all three subjects)
Biology: 4 (only Biology), 9 (Art and Biology), 5 (all three subjects)
Chemistry: 6 (only Chemistry), 5 (all three subjects)
Remember, you can always adjust the size of the circles based on the number of students in each subject to make the diagram clearer and more proportional.