Question

Discrete mathematics A software development company employs 100 computer programmers. Of them, 45 are proficient in Java, 30 in C++, 20 in Python, 6 in C++ and Java, 1 in Java and Python, 5 in C++ and Python, and 1 is proficient in all three languages. How many computer programmers are not proficient in any of these three languages?

Answer 1

Let n(A) = Number of computer programmers who are proficient in Java

     n(B) = Number of computer programmers who are proficient in C++

    n(C) = Number of computer programmers who are proficient in Python

So n (A $\cup$ B $\cup$ C) = Number of computer programmers who are proficient in any of these three languages

n(A $\cup$ B $\cup$ C)= n(A) + n(B) + n(C) - n(A$\cap$B) - n(B$\cap$C) - n(A$\cap$C) + n(A$\cap$B$\cap$C)

= 45 +30 +20 -6 -5 -1 +1 = 95-11 = 84

So, the number of programmers who are not proficient in any of these three languages = (100-84) = 16