In formal set theory, 3 sets determine 2³ = 8 regions. In general, n sets determine 2ⁿ regions. To see that the three sets in Example 2 determine 8 regions, you need to define a universal set that contains all three sets. For instance, the universal set could be "all people."

Veterans Day is celebrated each year on November 11^th. Have you ever wondered why that date was chosen?

In 1918, on the 11^th hour of the 11th day of the 11^th month, the Germans signed an armistice, or agreement to stop fighting, that ended World War I. It was originally declared Armistice Day, first celebrated in 1919, and became a national holiday in 1938. Following World War II and the Korean War, Armistice Day became known as Veterans Day to honor all American veterans.

The Veterans of Foreign Wars is an organization that serves American veterans to ensure that they are recognized for their service. Visit The VFW website to learn more about their efforts to help veterans and the community.

8. Number of veterans who earned a purple heart:

   

9. Number of veterans who earned a purple heart or a bronze star:

   

10. Number of veterans who earned a purple heart and a bronze star:

    

11. There was one veteran who earned all four medals.