Unless the residents of Glen Hills band together, the proposal to rezone that city will be approved. If it is the cit...

Ravi August 21, 2019

@ishadoshi,

Let's look at what the sentence in question is saying.

Neither new roads nor additional schools could be built without
substantial tax increases for the residents of Glen Hills.

"Without" tells us we can pick a part of the sentence, negate it, and
make it the sufficient condition. Let's pick the part that comes after
"without."

/Substantial tax increases - >

Now we put the other part of the sentence in the necessary condition

/new roads and /additional schools

/Substantial tax increases - >/new roads and /additional schools

New roads or additional schools - >substantial tax increases

/STI - >/NR and /AS

AS or NR - >STI

Does this make sense? When it's saying neither new roads nor
additional schools, this means that you're negating both of these
things and putting "and" between them.

Let us know if you have any other questions!

Anna20 May 30, 2020

So I diagrammed the last few sentences as ANR -- OS and CR. Then the last sentence as not STI -- not NR and not AS. I am missing the connection about how CR (crowded roads) automatically leads to new roads being built and a STI?

Many thanks for your help!

Anna20 June 2, 2020

Please can I follow up on this. Thank you!

Alaine July 23, 2020

Hi I also have a question on this same sentence. The rule tells us we should make the part of the sentence after 'Without' the necessary then negate the other part of the sentence and make it the sufficient. But it doesn't make sense (No NR + No NS > STI). But you showed the opposite, so can we make either part the s/n?

shunhe July 28, 2020

Hey everyone,

Thanks for the question! So first, let me talk about the connection between crowded roads and new roads being built and STI. The connection between crowded roads and new roads being built is given to us in the part that tells us that “the increased population…would certainly result in roads so congested that new roads would be built.” Since the roads WOULD be built, we know that the road congestion will lead to new roads. And then we’re told that neither new roads nor additional schools could be built without substantial tax increases, which is what links STI to all of that.

As for how to diagram that sentence: so the rule with “without” is correct, though kind of tricky to use in this case. But think about it this way: what does it mean to say that without the tax increases, we can’t have new roads or additional schools? Well, it means that if we don’t have the tax increases, we won’t get the new roads or additional schools! So that’s how we can diagram that sentence as

~STI —> ~NR & ~AS

Now let’s take the contrapositive of this sentence, which is

NR v AS —> STI

So this is actually going to match up with that rule you just cited. First, we take the part after without and make it the necessary, which is STI (which you also diagrammed. But now we have to negate the other part and put it in the sufficient. Well, what’s the other part of the sentence? It’s “neither new roads nor additional schools could be built.” So in other words, that part is

~(NR v AS)

So we negate that entire part and put it in the sufficient

~~(NR v AS) —> STI

And the double negatives cancel out so we get

NR v AS —> STI

which is what I diagrammed above. You erred in your representation of the other part of the sentence. You can make either part the S/N, as long as you follow the same negation rules, since these are contrapositives:

NR v AS —> STI
~STI —> ~(NR v AS)

Hope this helps! Feel free to ask any other questions that you might have.