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Problem on Set... how some of the number of students be distributed on venn diagram..

Problem:

In a class of 40 students, 17 have ridden an airplane, 28 have ridden a boat. 10 have ridden a train, 12 have ridden both an airplane and a boat. 3 have ridden a train only and 4 have ridden an airplane only. Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three.

Let Sets: A = airplane, B= Boat, T = train

I understand some of the number of students to be on the parts of the circles intersecting... there is a little bit confusing on the example given and the solution also... i tried to fix it on (A intersection B )

in the (A intersection B) = the number of students has ridden A and B...

my problem is how it was being separated in to 8 and 4... i could not get the rationale over that part...

thanks for your help mathematicians..

Re: Problem on Set... how some of the number of students be distributed on venn diagr

The number covered by A and B will be 17+28 - 12 = 33. (Minus 12 since it's included twice in the 17 and the 28.)

The number covered by A, B and T will be 33 + 3 = 36, leaving 4 outside A, B and T.

Easy from there.

Re: Problem on Set... how some of the number of students be distributed on venn diagr

Not too logical... But it s ok

Re: Problem on Set... how some of the number of students be distributed on venn diagr

Looks logical to me, and let me know if you happen to find something easier.

Once you know that there are 4 outside A, B and T you know that there are 4 in the common intersection of A, B and T, (which is what you asking).

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Re: Problem on Set... how some of the number of students be distributed on venn diagr