Amid students in a certain Capstone group, 60% have taken Linear Algebra, 50% have taken Calculus 3, and 30% have taken both. What portion of the students ... a. did not take Calculus 3? b. did not take either Linear Algebra or Calculus 3? c. took Linear Algebra but not Calculus 3? d. took Calculus 3 but not Linear Algebra?

a) 50%

b) 20%

c) 30%

d) 20%

Step-by-step explanation:

The total number of students will be 100%.

Let L be Linear Algebra and C be Calculus 3.

a) Those not taking C = 100% - those taking C = 100% - 50% = 50%

b) 60% take L but out of this, 30% take C also. Therefore, 60 - 30 = 30% take L only.

Applying the same to C, 50 - 30 = 20% take C only.

Total proportion of students taking any course at all = 30 + 30 + 20 = 80%.

Those not taking either = 100 - 80 = 20%

c) From the explanation in b) above, those taking L but not C are those taking L only = 30%

d) From the explanation in b) above, those taking C but not L are those taking C only = 20%