To find the outcomes that belong to event [tex]\( A \)[/tex] (the place is a city) or event [tex]\( B \)[/tex] (the place is in North America), we will analyze each place listed in the table and check if it satisfies either condition.
Here is the given information in a structured form:
- India: Not a city, Not in North America
- Tokyo: Is a city, Not in North America
- Chicago: Is a city, Is in North America
- Peru: Not a city, Not in North America
- Miami: Is a city, Is in North America
- Canada: Not a city, Is in North America
- Mexico: Not a city, Not in North America
Next, we determine which places satisfy being a city ([tex]\( A \)[/tex]) or being in North America ([tex]\( B \)[/tex]):
1. India: Does not satisfy [tex]\( A \)[/tex] or [tex]\( B \)[/tex].
2. Tokyo: Satisfies [tex]\( A \)[/tex].
3. Chicago: Satisfies both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
4. Peru: Does not satisfy [tex]\( A \)[/tex] or [tex]\( B \)[/tex].
5. Miami: Satisfies both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
6. Canada: Satisfies [tex]\( B \)[/tex].
7. Mexico: Does not satisfy [tex]\( A \)[/tex] or [tex]\( B \)[/tex].
So, the places that satisfy either [tex]\( A \)[/tex] or [tex]\( B \)[/tex] (or both) are:
- Tokyo
- Chicago
- Miami
- Canada
Next, compare this list with the provided options:
- A: \{Tokyo, Chicago, Miami\}
- B: \{Tokyo, Chicago, Miami, Canada, Mexico\}
- C: \{Chicago, Miami\}
- D: \{Chicago, Miami, Canada, Mexico\}
Option A is missing Canada.
Option B includes Mexico, which does not satisfy [tex]\( A \)[/tex] or [tex]\( B \)[/tex].
Option C is missing Tokyo and Canada.
Option D includes Mexico, which does not satisfy [tex]\( A \)[/tex] or [tex]\( B \)[/tex].
Considering the list we derived (Tokyo, Chicago, Miami, Canada), none of the provided options exactly match our list. Thus, the correct answer is:
[tex]\[ \text{None} \][/tex]
