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a set theory question (venn diagram)?
In a certain School, the pupils have to study Mathematics, Science or Geography. Each pupil must study at least one of the three subjects. Among a group of 40 pupils , 20 are studying Mathematics, 22 Science and 28 Geography; 12 are studying Mathematics and Science,14 are studying Science and Geography and 15 are studying Mathematics and Geography. How many pupils are studying all the three subjects ? if you could please tell me the step by step, thank you (i wont forget to give 5 stars)
1 Answer
- cidyahLv 74 years agoFavorite Answer
(Answer without using Venn diagram)
A = math
B = Science
C = Geography
n( A & B & C) = n(A) + n(B)+n(C) - n(A & B) - n (B & C) - n (A & C) + n (A & B & C)
40 = 20+22+28 -12-14-15 + n(A & B & C)
n(A & B & C) = 11
Venn diagram:
Math & Science = 12
x+(5) = 12
Science & Geography = 14
x+(6)=14
Math & Geography = 15
x+(4) = 15
(5) = 12-x
(6) = 14-x
(4) = 15-x
(1) = 20-(4)-(5)-x = 20-(15-x)-(12-x)-x = 20-15+x-12+x-x = x-7
(2)= 22-(5)-(6)-x = 22-(12-x)-(14-x)-x = 22-12+x-14+x-x = x-4
(3) = 28-(4)-(6)-x = 28-(15-x)-(14-x)-x = 28-15+x-14+x-x = x-1
40 = (1)+(2)+(3)+(4)+(5)+(6)+x
40 = (x-7)+(x-4)+(x-1)+(15-x)+(12-x)+(14-x)+x
x= 11 (number of students enrolled in all subjects)
