Venn diagram problem
P only=33-18-x
B only =26-17-x
C only =25-19-x
15-x+9-x+6-x+8+10+9+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
Can someone show me the calculation. The ans is 3.
P only=33-18-x
B only =26-17-x
C only =25-19-x
15-x+9-x+6-x+8+10+9+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
physics = 33 - (10-x) - (8-x) - x
chem = 25 - (10-x) - (9-x) - x
bio = 26 - (9-x) - (8-x) - x
physics + chem + bio = 63
63 = 30 + 9x
33/9 = x
x = 3.6....
we cant take 18 - x and subtract with 33 because its the collection of physics and chem, phy and bio students so we have to subtract the common students
P only=33-18-x
B only =26-17-x
C only =25-19-x
15-x+9-x+6-x+8+10+9+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
B only =26-17-x
C only =25-19-x
16-x+7-x+6-x+8+11+4+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
(I dont think I'm right)
In this problem, we have three sets: Physics (P), Chemistry (C), and Biology (B). We are given the following information:
- The number of students studying Physics (n(P)) is 33.
- The number of students studying Chemistry (n(C)) is 25.
- The number of students studying Biology (n(B)) is 26.
- The number of students studying Physics and Chemistry (n(P ∩ C)) is 10.
- The number of students studying Biology and Chemistry (n(B ∩ C)) is 9.
- The number of students studying Physics and Biology (n(P ∩ B)) is 8.
- The number of students studying none of the three subjects (n(P' ∩ C' ∩ B')) is equal to the number of students studying all three subjects. Let's denote this as x.
We can use the Principle of Inclusion-Exclusion to find the number of students who study all three subjects:
n(P ∪ C ∪ B) = n(P) + n(C) + n(B) - n(P ∩ C) - n(P ∩ B) - n(B ∩ C) + n(P ∩ C ∩ B)
Plugging in the given values, we have:
63 = 33 + 25 + 26 - 10 - 8 - 9 + x
Simplifying the equation, we have:
63 = 67 + x
Subtracting 67 from both sides, we get:
x = -4
Since the number of students cannot be negative, it means there was an error in the given information or statements. There cannot be a negative number of students studying all three subjects.
Hence, the given problem cannot be solved with the provided information.