1. GREEN UNIVERSITY OF
BANGLADESH
PRESENTATION ON : DISCRETE MATHEMATICS
COURSE CODE : CSE 101
Presented To,
Prof. Dr. Md. Abdur Razzaque
Chairperson
Dept. of CSE, GUB
Presented By,
Md. Reazul Islam
Id: 192002041
Section: DB
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2. PROBLEM :
• There are 2504 computer science students at a school.
• Of these, 1876 have taken a course in Java,
• 999 have taken a course in Linux,
• And 345 have taken a course in C.
• Further, 876 have taken courses in both Java and Linux,
• 231 have taken courses in both Linux and C,
• And 290 have taken courses in both Java and C.
• If 189 of these students have taken courses in Linux, Java, and C,
• How many of these 2504 students have not taken a course in any
of these three programming languages ?
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3. SOLUTIONS :
3
The shaded region
represents all the students
who have taken either one
of the courses.
J ⋃ L ⋃ C
But we are interested in finding the # of
students who lie outside this region.
4. SOLUTIONS :
|⋃|= # of Computer Science Students = 2504
|J| = # who have taken Java = 1876
|L| = # who have taken Linux = 999
|C|= # who have taken C = 345
|J⋂L| = # who have taken Java and Linux = 876
|L⋂C|= # who have taken Linux and C = 231
|J⋂C|= # who have taken Java and C = 290
|J⋂L⋂C| = # who have taken all 3 courses = 189
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5. SOLUTIONS :
1st step is to determine the # of students who have taken
either one of the 3 courses.
|J⋃L⋃C| = |J|+|L|+|C|- J⋂L|-|L⋂C|-|J⋂C|+|J⋂L⋂C|
= 1876 + 999 + 345 – 876 – 231 – 290 +
189
= 2012
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6. SOLUTIONS :
|𝐽𝑈𝐾𝑈𝐿|= # of students who have taken neither of the class
|𝐽𝑈𝐾𝑈𝐿| = |u|-|𝐽𝑈𝐾𝑈𝐿|
= 2504 – 2012
= 492 (Students have not taken a course In
any of the Languages)
Result is : 492.
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