guerrero25 wrote:
mridulparashar1 wrote:
Hi guerrero25,
There are 2 forumulaes
T = A+B+C - (Sum of 2 groups) + ( Sum of all three groups) + Neither
and T = A+B+C - (Sum of exactly 2 groups) - 2( sum of all three groups) + Neither
In this Q, Neither = 0
T = 14+10+11
35= 14+10+11 - x + 3 +0
x =3
Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes.
Hello Mridul ,Thanks for the explanation . Could you elaborate more when you say "Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes"..I could not understand the difference .
thanks again !
To understand the two different formulas, look at the diagram given here:
Attachment:
SetsThree_1_23Sept.jpg [ 20.19 KiB | Viewed 7972 times ]
A - No of people in set A = a + d + e + g
B - No of people in set B = b + d + g + f
C - No of people in set C = c + e + g + f
Notice that Total = a + b+ c + d + e + f + g
But depending on the given data, we often don't have values for a, b, c etc separately. When the question says, Math class has 14 students, it means a + d + e + g = 14. Similarly, if English class has 10 students, it means b + d + g + f = 10 and so on...
So we need to subtract the things we have counted twice/thrice. Note that if we write 14 + 10, we have already counted d and g twice here.
When we add A + B, we have counted (d +g) twice so we need to subtract it out once.
When we add C to it as well, we have counted (e + g) and (f + g) twice too so we need to subtract them out as well.
But when we do this, we have subtracted the g region 3 times and hence, it's not accounted for now. So we add it back.
This is how you get
T = A+B+C - (Sum of 2 groups) + ( Sum of all three groups) + Neither
On the other hand,
If after adding A + B + C, you subtract the region which is common to
ONLY two sets i.e. d, e and f, then you still need to subtract the g region twice since it is present in A, B and C.
That is how you get the formula:
T = A+B+C - (Sum of
ONLY 2 groups) - 2*( Sum of all three groups) + Neither
The formula to use depends on what data is given in the question.
To avoid confusion, it is a good idea to use venn diagrams instead.