Questions: Let J equal the set of countries who have won more than 3000 medals overall. Write the set J using the roster method. Let the universal set consist of the 10 countries listed in the table. Use the country abbreviations US, SU, GB, G, F, I, S, C, R, and EG when writing the set.

Let J equal the set of countries who have won more than 3000 medals overall. Write the set J using the roster method. Let the universal set consist of the 10 countries listed in the table. Use the country abbreviations US, SU, GB, G, F, I, S, C, R, and EG when writing the set.

Transcript text: Let $J$ equal the set of countries who have won more than 3000 medals overall. Write the set $J$ using the roster method. Let the universal set consist of the 10 countries listed in the table. Use the country abbreviations US, SU, GB, G, F, I, S, C, R, and EG when writing the set.

Solution

Solution Steps

To determine the set $ J $ using the roster method, we need to identify the countries from the given table that have won more than 3000 medals overall. We will iterate through the list of countries and their combined total medals, and select those with a total greater than 3000. Since none of the countries listed have more than 3000 medals, the set $ J $ will be empty.

Step 1: Identify the Countries

We are given a list of countries along with their total Olympic medals. The countries and their respective total medals are as follows:

$ \text{US} = 2681 $
$ \text{SU} = 1204 $
$ \text{GB} = 806 $
$ \text{G} = 782 $
$ \text{F} = 780 $
$ \text{I} = 663 $
$ \text{S} = 627 $
$ \text{C} = 526 $
$ \text{R} = 521 $
$ \text{EG} = 519 $

Step 2: Determine the Set $ J $

We need to find the set $ J $ of countries that have won more than $ 3000 $ medals. By examining the total medals for each country, we see that none of the countries listed have a total greater than $ 3000 $.

Step 3: Conclusion

Since no countries meet the criteria of having more than $ 3000 $ medals, the set $ J $ is empty.