# If Center 3 recycles glass, then which one of the following kinds of material must Center 2 recycle?

Wood and Newsprint

Why isn't the converse true of "If a center recycles wood, then it also recycles newsprint". I watched the vids for the game set up and explanation of this question but I fail to understand why the opposite isn't true and why the answer to this question could not also be wood. Thanks.

5 Replies

Mehran on December 3, 2016

@varcity64 because the rules of Sufficient & Necessary tell us otherwise.

We can create the contrapositive of any S & N statement by reversing AND negating:

S ==> N
not N ==> not S

There are only two ways to validly apply a general principle:

(1) Invoke S to conclude N (postive argument structure)

(2) Negate N to conclude not S (contrapositive argument structure)

For you to take the existence of the necessary condition, in this case newsprint, to conclude the existence of the sufficient condition, in this case wood, would be flawed logic.

Remember, don't just reverse!

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

RenÃ¡ta on August 23, 2019

there is no way to answer this question because I can only recycle plastic in center3 because it can be recycle in only one center and 1st makes same as 2nd... but I can't make glass where is plastic so it can't be true...

Ravi on August 23, 2019

Let's take a look at this question.

If G is in 3, we know P can't be in 3. We also know that P can't be in
2 since if something's in 2, it's also in 1 and there's only one P.
This means P must be in 1.

We know that neither G nor P can be in 2 because whatever is in 2 must
be in 1.This leaves us with 3 pieces that could potentially be in 2.
The 3 pieces are N, T, and W. There are 3 possible combinations for
these pieces:

WN
WT
NT

Would WN work? Yes, it would. Also, if there's a W, there's an N, so
this rule is satisfied with this combination.

What about WT? This wouldn't work because it would violate the rule of
there being and N with any W.

Would TN work? Yes, TN would work and we could have it in both 2 and
1. This means that both WN or NT would work. We were asked which
material 2 must recycle, and we see that in both cases, N is in 2, so
N is what must be in 2. This leads us to (B), which is the correct

Does this make sense? Let us know if you have any other questions!

Dominic on August 9, 2020

Why can't glass be in 2?
1-PGT 2-GT 3-GWN
Is this not valid? What is in 2 has to be in 1 but what is in 1 doesn't have to be in 2?

Victoria on August 13, 2020

Hello, happy to help!

Glass cannot be in Center 2 in your setup here because plastic is recycled at Center 1 and Rule 3 tells us that the one Center that recycles plastic does not also recycle glass.

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