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In a class of 25 students, 12 have taken mathematics, 8 have taken mathematics and computer science. The number of students who have taken computer science but NOT mathematics is:

In a class of 25 students, 12 have taken mathematics, 8 have taken mathematics and computer science. The number of students who have taken computer science but NOT mathematics is: Correct Answer 13

Concept:

Let A and B denote two sets of elements.

n(A) and n(B) are the numbers of elements present in set A and B respectively.

n(A - B) is the number of elements present in A but NOT in B.

n(B - A) is the number of elements present in B but NOT in A.

n(A ⋃ B) is the total number of elements present in either set A or B.

n(A ⋂ B) is the number of elements present in both the sets A and B.

 
  • n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B)
  • n(A - B) = n(A) - n(A ⋂ B)
  • n(B - A) = n(B) - n(A ⋂ B)

 

Solution: 

Let A and B be the sets of students who have taken Mathematics and Computer Science respectively.

Given: n(A ⋃ B) = 25, n(A) = 12 and n(A ⋂ B) = 8.

Calculation:

n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B)

⇒ 25 = 12 + n(B) - 8

⇒ 25 = 4 + n(B)

⇒ n(B) = 25 - 4 = 21

And the number of students who have taken computer science but NOT mathematics is:

n(B - A) = n(B) - n(A ⋂ B) = 21 - 8 = 13.

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