Question

Each person, in an IT department of 60 people, works on at least one of 3 major projects: system security, program implementation, platform development. 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. How many people work only on system security and program implementation (i.e., not all three projects)?
Answer either: 4, 5 or 6

Answer 1

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=$\text{A}$, $\text{A}=23$

let people in  program implementation be=$\text{B}$,  $\text{B}=28$

let people in platform development be=$\text{C}$, $\text{C}=26$

persons working in $\text{A}$ and $\text{B}$= $\text{A}$∩$\text{B}$, $\text{A}$∩$\text{B}$=$7$

persons working in $\text{B}$ and $\text{C}$= $\text{B}$∩$\text{C}$, $\text{B}$∩$\text{C}$=$12$

persons working in $\text{C}$ and $\text{A}$= $\text{C}$∩$\text{C}$=

persons working in $\text{A}$,$\text{b}$ and $\text{C}$=$\text{A}$∩$\text{B}$∩$\text{C}$, $\text{A}$∩$\text{B}$∩$\text{C}$=6

Now,

we know that

$\text{A}$∪$\text{B}$∪$\text{C}$= $\text{A}$ +$\text{B}$+$\text{C}$-$\text{A}$∩$\text{B}$-$\text{B}$∩$\text{C}$-$\text{C}$∩$\text{A}$+$\text{A}$∩$\text{B}$∩$\text{C}$

on putting values,

60=23+28+26-7-12-$\text{C}$∩$\text{A}$+6

$\text{C}$∩$\text{A}$=64-60

$\text{C}$∩$\text{A}$=4

hence, the number of persons working in system security and program implementation are=4

Answer 2

Answer:

6

Step-by-step explanation:

first take 3+3=6+12=18+28=46+7=53+12=65

65-60=5 five is answer