In a technology seminar attended by 60 software engineers, 35 engineers know Python and 25… — State PSC Exam

In a technology seminar attended by $60$ software engineers, $35$ engineers know Python and $25$ engineers know Java. If $10$ engineers know both Python and Java, how many engineers know neither of these two programming languages?

Cevap: 10 engineers

Cevap

The number of engineers who know neither Python nor Java is 10.

The correct answer is 10. By taking the sum of Python knowers (

35

) and Java knowers (

25

) and subtracting those who know both (

10

), we obtain

50

engineers who know at least one language. Subtracting this from the total

60

seminar participants leaves

10

engineers who know neither language.

Adım Adım Çözüm

Find the total number of engineers who know at least one programming language

50 engineers know at least one language

Apply the two-set union formula:

n(A \cup B) = n(A) + n(B) - n(A \cap B) = 35 + 25 - 10 = 50

Calculate the number of engineers who know neither language

10 engineers know neither language

Subtract the number of engineers knowing at least one language from the total group size:

60 - 50 = 10

Anahtar Kavram

Two-Set Inclusion-Exclusion Principle and Complement of Sets

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