Operations of Sets

[Dennis Fai]

A study of 80 pupils was conducted on the modes of transportation when travel back to their hometowns. 25 pupils travel by train and 48 pupils travel by train or car. If 7 pupils travel by train and car, 5 pupils travel by bus and train, and 2 pupils travel by all three modes of transportation, how many pupils do travel by train or bus but not by car?

 

[HallsofIvy]

Do you understand what this is saying? Do you understand the difference between "48 pupils travel by train or car" and "7 pupils travel by train and car"? Do you see that 48- 7= 41 pupils either "travel by train but not by car" or "travel by car but not by train"?

I recommend a "Venn diagram".

Draw three overlapping circles, representing "travel by car", "travel by train", and "travel by bus". There are three possible methods of travel and since a given pupil may or may not use that method, there are \(\displaystyle 2^3= 8\) sections (including outside all three circles- did not use any or these methods). There will be a section where all three circles overlap. Since "2 pupils travel by all three modes of transportation" write the number 2 in it. There will be a section where "travel by train" and "travel by car" only overlap. Since "7 pupils travel by train and car", but two of those also traveled by bus, 7- 2= 5 will go in that section.