The set of gold medalists in the 2014 Winter Olympic games in set builder notation.

I don't get what I'm supposed to do.

your answers are good, except for the gold medalists.

That would just be a list of names of the winners.
If such a list is hard to determine, or too long to be easily listed, or if the actual names are unimportant, then I'd just go with

A= {x l x was a gold medalist in the 2014 Winter Olympic games}

Am I supposed to know how many gold medalists were in the 2014 winter Olympic games?

Like when they ask for set builder notation for vowels, I get it is {a,e,i,o,u}
A = {x l x is a vowel}

Or I just write it like A= {x l x is the number of gold medalists in the 2014 Winter Olympic games).

My second and last question:

For { x l x is a digit in the number 351,646}, the roster would be written as {2,3,4,5,6} right?

To represent the set of gold medalists in the 2014 Winter Olympic games using set builder notation, you need to specify the properties or conditions that the elements of the set should satisfy.

Here's a step-by-step process to help you determine the set of gold medalists:

1. Find a reliable source that provides the complete list of gold medalists for the 2014 Winter Olympic games. This could be an official Olympic website, a sports news outlet, or any trusted source that provides accurate information.

2. Identify the specific event or events in which you are interested. The Winter Olympic games involve various sports and disciplines, so you need to decide which events' gold medalists you want to include in your set. For example, you might choose to include sports like figure skating, hockey, skiing, and snowboarding.

3. Once you have the list of gold medalists for the chosen events, analyze the properties that make them gold medalists. These properties could include factors like winning the highest score or time, being at the top of the leaderboard, or having the best performance in a specific category or discipline.

4. Use set builder notation to represent the set. Set builder notation typically follows the form {x | P(x)}, where x represents the elements of the set, and P(x) represents the properties or conditions that the elements must satisfy. For example, if you are interested in the gold medalists in figure skating and the gold medals were awarded based on the highest score, you could write the set as follows: {x | x is a gold medalist in figure skating and achieved the highest score}.

Remember that the specific notation might depend on the context and requirements of the problem, so adapt the notation accordingly.

Note: As an AI, I don't have real-time data access, so I can't provide you with the exact set of gold medalists in the 2014 Winter Olympic games. However, by following the steps above, you can find the information and represent it using set builder notation yourself.