Question

there are 75 students in the Travel Club. They discover that 27membershavevisited Mexico34
have visited Canada 12 have been to England, 18 have visited both Mexico and Canada 6 have
been only to England, and 8 have been only to Mexico,some club members have not been to any 3 foreign countries, curiously and equal number to all three countries
How many students have been to all the countries
b) How many students have been only to Canada?
and P such that OQ-OR- RS - SP
point T ber​

Answer 1

Answer:

Step-by-step explanation:

Total students = 75

Visited Mexico  = 27   = M

Visited Canada = 34  = C

Visited England = 12  = E

Visited Mexico & Canada = 18   = M∩C

Only to England = 6  =   E only

Only to Mexico = 8 =  M only

Visited no country = X  

Visited all country = X    M∩C∩E

Total Students = M + C + E  -  M∩C -  M∩E - E∩C  + M∩C∩E  + No country

=> 75 = 27 + 34 + 12 - 18 -  M∩E - E∩C + X + X

=>  M∩E + E∩C = 2X - 20

Only Mexico = M - M∩E  - M∩C + M∩C∩E

=> 8 = 27 -  M∩E - 18  + X

=> M∩E = X + 1

Only England = E - M∩E  - E∩C + M∩C∩E

=> 6 = 12 - X -1 - E∩C + X

=>E∩C = 5

Only Canada = C - M∩C  - E∩C + M∩C∩E

=> Only Canada = 34 - 18 - 5 + X

=> Only Canada = 11 + X

M∩E + E∩C = 2X - 20

=> M∩E + 5 = 2X - 20

=> M∩E  = 2X - 25

M∩E = X + 1

=> 2X - 25 = X + 1

=> X = 26

its not possible that 26 people visited all countries

So some data is wrong

With Some different Data Solved

With changed data  

Total students = 40

Visited Mexico  = 17   = M

Visited Canada = 28  = C

Visited England = 10  = E

Visited Mexico & Canada = 12   = M∩C

Only to England = 3  =   E only

Only  to Mexico = 4 =  M only

Visited no country = X    

Visited all country = X    M∩C∩E

Total Students = M + C + E  -  M∩C -  M∩E - E∩C  + M∩C∩E  + No country

=> 40 = 17 + 28 + 10 - 12 -  M∩E - E∩C + X + X

=>  M∩E + E∩C = 2X + 3

Only Mexico = M - M∩E  - M∩C + M∩C∩E

=> 4 = 17 -  M∩E - 12  + X

=> M∩E = X + 1

Only England = E - M∩E  - E∩C + M∩C∩E

=> 3 = 10 - X -1 - E∩C + X

=>E∩C = 6

M∩E + E∩C = 2X + 3

=> M∩E + 6 = 2X +3

=> M∩E  = 2X - 3

M∩E = X + 1

=> 2X - 3 = X + 1

=> X = 4

Only Canada = C - M∩C  - E∩C + M∩C∩E

=> Only Canada = 34 - 18 - 5 + 4

=> Only Canada = 15