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?

Answer: 10 engineers

Answer

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.

Step-by-Step Solution

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

Key Concept

Two-Set Inclusion-Exclusion Principle and Complement of Sets

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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