Problem Solving with Sets:

In class we solved several challenging problems that involved set ideas. The two problems we ended class with were:

The Mailing List problem

Every one on my mailing list likes either mysteries or fantasy books. If there are 60 people on the list, and 45 like mysteries, and 39 like fantasy, how many do you think like both?

This is an interesting problem because there are several solution strategies.

The Breakfast Problem

Nine Students had juice for breakfast, but only two had nothing else.

The same number of students had juice and vereal (without eggs) as had cereal by itself

Only one student had everything that was offered for breakfast. She had juice, cereal and eggs

Five students had eggs, but only one had them withour anything else.

Eight students had no eggs at all.

How many students had something for breakfast?

This is an interesting problem because it introduced algebra ideas: The clue: The same number of students had juice and vereal (without eggs) as had cereal by itself relates two unknown quantities, which is one of the big ideas of algebra!