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.
Your Solution
Hints
�œ I want you to choose a state or province; then, write three yes or no questions that if I asked you them, I would be able to figure out the state you are thinking about. Try using a tree diagram to help organize this
his is a question I don't understand.
1. You need to choose one of those 7 states or provinces.
2. Think of three yes-or-no questions that someone could ask you that would help them figure out which state or province you'd chosen. The first question could be "Are there 7 letters in the name?" (If yes, then it would narrow it down to two choices.)
Check these sites for examples of tree diagrams.
http://www.google.com/search?source=ig&hl=en&rlz=1G1GGLQ_ENUS338&q=tree+diagram&aq=f&oq=&aqi=
To determine the element chosen from the set of northwestern states or provinces {Montana, Washington, Idaho, Oregon, Alaska, British Columbia, Alberta}, we can use a binary decision tree. A binary decision tree is a tree-like structure where each node represents a yes or no question, and the branches represent the possible answers (yes or no) to that question.
Here's a possible set of three yes or no questions that can be asked:
1. Is the chosen element located within the United States?
- If the answer is yes, we eliminate Alaska, British Columbia, and Alberta.
- If the answer is no, we eliminate Montana, Washington, Idaho, and Oregon.
2. Is the chosen element located along the coastline?
- If the answer is yes, we eliminate Montana and Idaho.
- If the answer is no, we eliminate Washington and Oregon.
3. Is the chosen element primarily known for its wilderness and natural beauty?
- If the answer is yes, the remaining element is Montana.
- If the answer is no, the remaining element is Washington.
By asking these three questions, we can narrow down the possibilities and determine the chosen element from the set.