Which one of the following is a complete and accurate list of the recycling centers in Rivertown any one of which cou...

jenks on February 24, 2016

I too have the same question

Mehran on February 25, 2016

This question is asking us to identify a complete and accurate list of recycling centers in Rivertown any one of which COULD recycle plastic.

So while you are correct that only one of the recycling centers recycles plastic, that one center can be either Center 1 or Center 3. Obviously, it cannot be both but that is not what this question is asking.

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Hope this helps! Please let us know if you have any other questions.

lindseyru on May 16, 2016

If center 1 and center 2 recycle the same material, how is it possible to have plastic in center 1 without violating the condition of plastic recycled only in one center?

Mehran on May 20, 2016

@lindseyru the reason is that Center 1 and Center 2 do not have to recycle the same material.

The second condition actually states, "Every kind of material that Center 2 recycles is also recycled at Center 1."

"Every" introduces a sufficient condition, so we would diagram this condition as follows:

2 âž¡ 1
not 1 âž¡ not 2

This DOES NOT mean Center 1 and Center 2 recycle the same material.

Center 1 is the necessary condition here so its existence tells us nothing else, i.e. it is possible that Center 2 recycles the same material, but it is also possible that it does not.

Therefore, it is possible that Center 1 recycles plastic and Center 2 does not.

Hope this helps! For a more in-depth review of these concepts, please review our Sufficient & Necessary lesson.

michellesheinker@gmail.com on March 21, 2020

Why do you automatically assume center 2 will recycle wood and newspaper when working out the hypothetical?

Dinora-Orozco on April 7, 2020

Hello, I have the same question as above. Why do you automatically assume that center 2 will recycle wood and newspaper?

NS1 on May 14, 2020

Same question as the inquiries above...Why do you automatically assume center 2 will recycle wood and newspaper? @mehran

ojwill2 on May 19, 2020

This is very confusing because if center 1 recycles plastic then center 2 also recycles it and then a rule is violated

Skylar on July 12, 2020

@Mcihelle @Dinora @Nigel, happy to help!

We want to see if P can be placed in Center 1. We know that Center 2 must have 2-3 materials and that whatever is in Center 2 must also be in Center 1. Since we don't/can't have P in Center 2, we must fill its two slots with other materials.
1: __ __ P
2: __ __
3: __ __ (__)

The remaining materials are G, N, T, and W. Rule #1 tells us that if we have W, we must also have N. To use all of the materials, these two must appear together somewhere, which leaves G and T as our other pair.

How do we know which pair (WN or GT) appears in Centers 1 and 2 and which appears in Center 3? Rule #3 tells us that the center that recycles P cannot also recycle G. In other words, P and G cannot appear at the same center. This means that W and N must be assigned to Centers 1 and 2, leaving G and T to be assigned to Center 3.

Does that make sense? Please let us know if you have any other questions!

Skylar on July 12, 2020

@ojwill2, happy to help!

Careful! Rule #2 says that "every kind of material that Center 2 recycles is also recycled at Center 1." In other words, everything at Center 2 is also at Center 1. However, not everything at Center 1 has to be at Center 2. Therefore, it is possible for plastic to be assigned only to Center 1 without breaking any rules.

Does that make sense? Please let us know if you have any other questions!