In a group of 40 students, all students study maths, 28 study biology and math, 20 students study geography and maths and x students study all three subjects.

a. Draw a venn diagram to represent the information above, showing in terms of x, the number of students in each subset
b. Determine the number of students who study all three subjects.

Help me please!!

M*B*G* = 8----------1

M*B =28----------2
M*G =20----------3
G= 3-1=12
B= 2=1=20
M=8

Where is the venn diagram

a. Here's a humorous representation of the Venn diagram:

```
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( ͡° ͜ʖ ͡° )
( _ )
```

In this Venn diagram, the left circle represents biology, the right circle represents geography, and the middle circle represents math.

b. To determine the number of students studying all three subjects, we need to find the intersection of all three circles. Based on the information provided, there are x students studying all three subjects.

Certainly! Let's start by creating the Venn diagram to represent the information given.

a. To draw the Venn diagram, we need three overlapping circles representing each subject: math, biology, and geography. We can label these circles as M (Math), B (Biology), and G (Geography).

Since all 40 students study math, we place the number 40 inside the circle M.

Since 28 students study both biology and math, we place the number 28 in the overlapping region of circles M and B.

Similarly, since 20 students study both geography and math, we place the number 20 in the overlapping region of circles M and G.

Lastly, we are given that "x" students study all three subjects, so we place the variable "x" in the region where all three circles overlap (M, B, and G).

The Venn diagram should now reflect the information given.

B
/ \
/ \
M --- G

b. To determine the number of students who study all three subjects, we need to find the value of "x."

We know that:
- 40 students study math (inside M).
- 28 students study both biology and math (overlapping M and B).
- 20 students study both geography and math (overlapping M and G).

To calculate the number of students who study all three subjects, we can use the principle of the inclusion-exclusion principle.

The formula is:
Total = M + B + G - (M ∩ B) - (M ∩ G) - (B ∩ G) + (M ∩ B ∩ G)

Substituting the given values into the formula:
40 = 28 + 20 - (M ∩ B) - (M ∩ G) - (B ∩ G) + x

We can simplify further:
40 = 28 + 20 - 0 - 0 - 0 + x
40 = 48 + x

To find the value of "x," subtract 48 from both sides of the equation:
x = 40 - 48
x = -8

Therefore, there is no value of "x" that satisfies the given conditions. This implies there are no students who study all three subjects.