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

4

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