Answer to Question #91606 in Discrete Mathematics for Ed

Question

According to information obtained from mathematics department regarding three mathematics units done by 100 students, those who are doing calculus are 45, those doing discrete are 49 and those doing statistics are 38. Those doing calculus and discrete are 17, those doing calculus and statistics are 12 and those doing the three units are 5. Use Venn diagram to find the number of students doing discrete and statistics but not calculus

Answer 1

Create a Venn diagram where circles C, B, and M respectively denote students doing calculus , discrete and statistics (Img1).

x6 Venn diagram area students doing discrete and statistics but not calculus

from the conditions of the problem we have the following equalities:

x1+x2+x4+x5 =45 students, those who are doing calculus

x3+x2+x5+x6 =49 students, those who are doing discrete

x7+x4+x5+x6 = 38 students, those who are doing statistics

x2+x5 = 17 students, those who are doing calculus and discrete

x4 +x5 = 12 students, those who are doing calculus and statistics

x5 = 5 students, those who are doing calculus and statistics and discrete

x1+x2+x3+x4+x5+x6+x7 = 100 all students

Find S sum of students doing calculus , doing discrete and doing statistics 

S = 45+49+38 = 132

S= (x1+x2+x4+x5) +(x3+x2+x5+x6) +( x7+x4+x5+x6) =

= (x1+x2+x3+x4+x5+x6+x7) +(x2+x5) +(x4+x5) + x6 =

= 100 +17+12 +x6 = 129 +x6

Therefore x6 = S-129 = 132-129 = 3

Answer : 3 students doing discrete and statistics but not calculus