(i) How Many students passed in at least one subjects. - (ii) How many students passed in English only? - (iii) How many students failed in all three subjects? -

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: Dec 2015

Let A denotes students passed in English.

B denotes students passed in Science.

and C denotes students passed in Mathematics.

|A| =80

|B| =60

|C| =50

|AՈB| =30

|AՈC| =15

|BՈC| =20

|A U B U C|=150

|AՈBՈC| =10

Students passed in at least one subjects

=|AՈB|+|AՈC|+|BՈC|

=30+15+20

=65

Hence, students passed in atleast one subject are 65

Students passed in English only

Passed in English only=|A|-[|AՈB|+|AՈC|+

=|A|-[|B|+|C|-|B Ո C|+|AՈBՈC|]

=80-[30+15+10]

=25

Hence, students passed in English only are 25.

Students failed in all three subjects

|A ̅ՈB ̅ՈC ̅|=150-(80+60+50) + (30+15+20)-10=60-62+20-2=10

So, 10 students failed in all three subjects.