Answer:
4
Step-by-step explanation:
Given: total persons in IT department=60,23 people work on system security, 28 work on program implementation, and 26 work on platform development. 7 people work on system security and platform development, 12 people work on program implementation and platform development, and 6 people work on all three projects.
To Find: number of people working only on system security and program implementation.
Solution:
let people in system security be=[tex]\text{A}[/tex], [tex]\text{A}=23[/tex]
let people in program implementation be=[tex]\text{B}[/tex], [tex]\text{B}=28[/tex]
let people in platform development be=[tex]\text{C}[/tex], [tex]\text{C}=26[/tex]
persons working in [tex]\text{A}[/tex] and [tex]\text{B}[/tex]= [tex]\text{A}[/tex]∩[tex]\text{B}[/tex], [tex]\text{A}[/tex]∩[tex]\text{B}[/tex]=[tex]7[/tex]
persons working in [tex]\text{B}[/tex] and [tex]\text{C}[/tex]= [tex]\text{B}[/tex]∩[tex]\text{C}[/tex], [tex]\text{B}[/tex]∩[tex]\text{C}[/tex]=[tex]12[/tex]
persons working in [tex]\text{C}[/tex] and [tex]\text{A}[/tex]= [tex]\text{C}[/tex]∩[tex]\text{C}[/tex]=
persons working in [tex]\text{A}[/tex],[tex]\text{b}[/tex] and [tex]\text{C}[/tex]=[tex]\text{A}[/tex]∩[tex]\text{B}[/tex]∩[tex]\text{C}[/tex], [tex]\text{A}[/tex]∩[tex]\text{B}[/tex]∩[tex]\text{C}[/tex]=6
Now,
we know that
[tex]\text{A}[/tex]∪[tex]\text{B}[/tex]∪[tex]\text{C}[/tex]= [tex]\text{A}[/tex] +[tex]\text{B}[/tex]+[tex]\text{C}[/tex]-[tex]\text{A}[/tex]∩[tex]\text{B}[/tex]-[tex]\text{B}[/tex]∩[tex]\text{C}[/tex]-[tex]\text{C}[/tex]∩[tex]\text{A}[/tex]+[tex]\text{A}[/tex]∩[tex]\text{B}[/tex]∩[tex]\text{C}[/tex]
on putting values,
60=23+28+26-7-12-[tex]\text{C}[/tex]∩[tex]\text{A}[/tex]+6
[tex]\text{C}[/tex]∩[tex]\text{A}[/tex]=64-60
[tex]\text{C}[/tex]∩[tex]\text{A}[/tex]=4
hence, the number of persons working in system security and program implementation are=4
