Given : 25 students failed in Mercantile law, 24 failed in Statistics, 32 failed in ACCOUNTANCY, 9 failed in Mercantile law alone, 6 failed in Statistics alone ; 5 failed in Accountancy and Statistics only and 3 failed in Mercantile law and Statistics only

To Find : (i) how many failed in all three subjects.

(ii) how many passed in ail the three subjects.​

Solution:

Failed in Mercantile   law  L =  25   =>  Passed in Mercantile   law  = 35

Failed in Statistics S  =  24   =>  Passed in Statistics  = 36

Failed in Accountancy A   =  32   =>  Passed in Accountancy  = 28

failed in Mercantile  law alone = 9

failed in Statistics alone  = 6

failed in Accountancy and  Statistics only  = 5

failed in Mercantile law and Statistics only  =  3

Failed in all three subjects =  L ∩ S ∩ A

failed in Mercantile  law alone  = L  - L∩ S - L ∩  A + L ∩ S ∩ A = 9

=> 16 + L ∩ S ∩ A = L∩ S +  L ∩  A

failed in Statistics alone  = S  - L∩ S - S ∩  A + L ∩ S ∩ A = 6

=> 18 + L ∩ S ∩ A =  L∩ S +  S ∩  A

failed in Accountancy and  Statistics only  = S ∩  A -   L ∩ S ∩ A = 5  

S ∩  A = L ∩ S ∩ A+  5  

18 + L ∩ S ∩ A =  L∩ S +  S ∩  A

=> 18 + L ∩ S ∩ A =  L∩ S  +  L ∩ S ∩ A+  5

=>  L∩ S  = 13

failed in Mercantile law and Statistics only   = L∩ S - L ∩ S ∩ A = 3

=> L∩ S =  L ∩ S ∩ A+  3

16 + L ∩ S ∩ A = L∩ S +  L ∩  A

=> 16 + L ∩ S ∩ A = L ∩ S ∩ A+  3  + L ∩  A

=>  L ∩  A = 13

16 + L ∩ S ∩ A = L∩ S +  L ∩  A

=> 16 + L ∩ S ∩ A = 13 +  13

=>  L ∩ S ∩ A = 10

failed in all three subjects. = 10

Failed in  Mercantile law  and accountancy only = L ∩  A -  L ∩ S ∩ A

= 13 - 10

=3

S ∩  A = L ∩ S ∩ A+  5   = 10 + 5 = 15

Failed in accountancy only = A - A∩ S - L ∩  A + L ∩ S ∩ A

= 32 - 15 - 13 + 10   =   14

Failed in any of the SUBJECT  = 9 + 6 + 14 + 3  + 5 + 3 + 10

=   50

Passed in all three subjects = Not failed in a any subject

= 60 - 50 = 10

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