Question

in a school of 300 students, 170 takes science, 230 takes Arts and every students takes at least science and arts. Draw a Venn diagram to illustrate these information . find the number of students taking both science and arts​

Answer 1

To find the number of students taking both Science and Arts, you can use the formula for the total number of students in two overlapping sets:

\[ \text{Total number of students} = \text{Students taking Science} + \text{Students taking Arts} - \text{Students taking both} \]

In this case, you have:

\[ 300 = 170 + 230 - \text{Students taking both} \]

First, sum up the number of students taking Science and the number taking Arts:

\[ 170 (Science) + 230 (Arts) = 400 \]

Now, to find the number of students taking both subjects, subtract the total number of students from this sum:

\[ 400 - 300 = 100 \]

So, 100 students are taking both Science and Arts.

For the Venn diagram, you can have two circles, one for Science and one for Arts, overlapping.

- In the Science circle, you'll have \( 170 - 100 = 70 \) (only taking Science)

- In the Arts circle, you'll have \( 230 - 100 = 130 \) (only taking Arts)

- In the overlapping section, you'll have 100 (taking both Science and Arts)