Consider the set of northwestern states or provinces

{Montana, Washington, Idaho, Oregon, Alaska, British
Columbia, Alberta}. If a person chooses one element,
show that in three yes or no questions, we can determine
the element.

You can try to draw a tree diagram using three appropriate questions with eight possible outcomes.

To determine the element chosen from the set of northwestern states or provinces {Montana, Washington, Idaho, Oregon, Alaska, British Columbia, Alberta}, we can use the following questions:

1. Is the chosen element located in the United States? (yes/no)
- If the answer is "yes," we can narrow down the possibilities to Montana, Washington, Idaho, Oregon, and Alaska.
- If the answer is "no," we can narrow down the possibilities to British Columbia and Alberta.

2. Does the chosen element share a border with the Pacific Ocean? (yes/no)
- If the chosen element is in the United States and the answer is "yes," the possibilities are Washington, Oregon, and Alaska.
- If the chosen element is in Canada and the answer is "yes," the possibility is British Columbia.
- If the chosen element is in the United States and the answer is "no," the possibility is Montana.
- If the chosen element is in Canada and the answer is "no," the possibility is Alberta.

3. Does the chosen element share a border with Canada? (yes/no)
- If the chosen element is in the United States and the answer is "yes," the possibility is Idaho.
- If the chosen element is in the United States and the answer is "no," the possibility is Oregon.
- If the chosen element is in Canada and the answer is "yes," the possibility is British Columbia.

By asking these three yes or no questions, we can determine the element chosen from the set of northwestern states or provinces.