# Sets and Classrooms in a Primary School

## How many classrooms in the primary school have white boards, smart boards, or no boards?

What are events A and B denoting in this scenario?

What is the number of classrooms represented by each of the following events?

(a) The selected classroom has both boards.

(b) The selected classroom has smart board only.

(c) The selected classroom has either a white board or a smart board but not both.

## Sets and Classrooms Representation

The number of classrooms with white boards: 20

The number of classrooms with smart boards: 18

The number of classrooms with no boards: 2

Every year, an inspector visits a primary school with 35 classrooms, where 20 classrooms have white boards, 18 classrooms have smart boards, and 2 classrooms have no boards.

Event A represents the selection of a classroom with a white board, while Event B represents the selection of a classroom with a smart board.

Now, let's find the number of classrooms represented by each event:

(a) The event that the selected classroom has both a white board and a smart board can be represented by the intersection of sets A and B. Since there are 20 classrooms with white boards and 18 classrooms with smart boards, there can be at most 18 classrooms with both boards.

(b) The event that the selected classroom has a smart board only can be represented by the elements in set B but not in set A. Since there are no classrooms with smart boards only in this scenario, the number of classrooms with smart boards only is 0.

(c) The event that the selected classroom has either a white board or a smart board but not both can be represented by the union of (A - B) and (B - A). This means there are 2 classrooms with white boards only and 18 classrooms with smart boards only. Therefore, the total number of classrooms represented by this event is 2 + 18 = 20.

Thus, using set notation and set operations, we can determine the number of classrooms represented by different events based on the presence of white boards, smart boards, and no boards in the primary school.