The Intersection of Programmers and Languages

a) What portion of programmers know Python or know Java?

Write your answer in Blank 1

b) What portion of programmers does not know Python and does not know Java?

Write your answer in Blank 2

Answer for Blank 1: 86%

Answer for Blank 2: 14%

Using set theory, we can analyze the data provided and understand the percentages of programmers who know Java and Python as well as those who do not know either language.

Explanation:

This problem can be solved by considering the principles of set theory and the concept of the union of sets. Let's break it down:

1. Percentage of programmers who know Java: 72%

2. Percentage of programmers who know Python: 67%

3. Percentage of programmers who know both languages: 53%

Now, let's calculate the answers to the questions:

For Blank 1:

The portion of programmers who know either Java or Python (or both), which is the union of the two sets, can be found using the formula A U B = A + B - (A ∩ B), where A and B are the individual sets, and A ∩ B is the intersection of A and B.

Plugging in the given values: 72% + 67% - 53% = 86%

So, 86% of the programmers know either Java or Python.

For Blank 2:

To find the portion of programmers who do not know either Java or Python, we simply subtract the percentage that knows at least one of the languages from 100%.

Calculation: 100% - 86% = 14%

Therefore, 14% of the programmers do not know either language.

By understanding these percentages and applying set theory concepts, we can gain insights into the knowledge distribution among programmers in the firm.