Read pages 26-28 Examples 2 and 3 in your textbook, Principles of Mathematics 12 .

Complete the Your Turn question on page 27 and page 28 for more practice in determining the number of elements in a set.

Click here to verify your answers .


A frequent task in Math 30-2 is to analyze the solution to a given problem, determine if the solution contains any mistakes, and identify the mistakes. The next example shows a type of mistake you might be asked to identify when dealing with the intersection and union of sets.


Charles solved the following problem:

A total of 48 students were asked how they travel to school.

  • 31 students drive a car.
  • 16 students take a bus.
  • 12 students do not drive a car or take a bus.
  • Some students drive a car or take a bus.

Determine how many students do not take a bus to school.

Charles' Solution: The total of the three numbers is 59. So, I knew that the region for students who take a bus overlaps the region for students who drive a car. I drew a Venn diagram with 31 students in the car region and 16 students in the bus region. 15 students drive a car but do not take a bus, 12 students do neither. So, 27 students do not take a bus. Is Charles correct? Justify your answer.  


Charles' answer is not correct.

Some students take a bus but do not drive a car. These regions should overlap only partially. Because Charles drew B as a subset of C , the total number of students in Charles' diagram is only 43.

An accurate diagram to represent this data is shown below.