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JA1. More on Sets

  1. If A is the set of people who got jobs in the IT sector and B is the set of people who got jobs. Describe the people in each of the following sets

    • (a) A ∩ B: People who got jobs in the IT sector.
    • (b) A ∪ B : All people who got jobs.
    • © A − B: People who got jobs in the IT sector.
    • (d) B − A: All People who got jobs except those who got jobs in the IT sector.

  2. Suppose that A is the set of people living in the USA and B is the set of people having a house in Canada. Express each of the following sets in terms of A and B using set operations

    • (a) the set of people living in the USA and having a house in Canada
    \[A ∩ B\]
    • (b) the set of people living in the USA who are not having a house in Canada
    \[A − B\]
    • © the set of people who either live in the USA or have a house in Canada
    \[A ∪ B\]
    • (d) the set of people who are either non-US residents or do not own a house in Canada
    \[A' ∪ B'\]

  3. An IT company offered two benefits for the employees 750 of the employees take the privilege of cabs. 900 of them take breakfast privilege. If 530 employees take both benefits

A B A ∩ B A’ ∩ B’
Cab Breakfast Both None
750 900 530 60
  • how many employees work in the company if there are 60 employees who do not take any benefits?
\[ \begin{align} |A ∪ B| & = |A| + |B| - |A ∩ B| \\ & = 750 + 900 - 530 \\ & = 1120 \end{align} \]
\[ \begin{align} |U| & = |A ∪ B| + |(A ∪ B)'| \\ & = |A ∪ B| + |A' ∩ B'| \\ & = 1120 + 60 \\ & = 1180 \end{align} \]
  • Which concept do you use to calculate the number of employees in the company? You can either use a Venn diagram or you can use the principle of inclusion and exclusion

We use the principle of inclusion and exclusion to calculate the number of employees in the company, as the previous answer explains, the total number of employees is the sum of the number of employees who take at least one benefit and the number of employees who do not take any benefits at all.