Hello, so for this question and many others like these, I'am to get down to two answers always, but I always get them mixed up. I knew that if U exist R does not, but the answer was not R then U? The only reason I picked U - > not R is because U exists? Can someone break this down so I can understand this
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I think maybe I'll go through my thought process when I approach these questions and perhaps that'll help?
We have 3 premises (2 given, 1 for us to determine) + a conclusion (given). They are as follows:
P1: R -> Not S P2: ( ) P3: T - > S
C: T - > U
When I see this, I immediately realize that no matter what, the goal is to figure out a way to get T - > U. This means that our chain should begin with T.
T leads to S according to P3. I see S only in P1, but in negated form. So, I use the contrapositive to reach the following: S - > Not R.
At this point I have linked up everything given. Now we need to connect what we have such that it leads to U.
That would mean: Not R - > U. (and its contrapositive).
I think that trying to follow the chain is the easiest and most intuitive way of approaching these questions. And also, trying to figure out a way that the added premise will result in the conclusion we are given.
Please let me know if this was helpful. If not, I'd be happy to look at this again with you!
LucasDecember 19, 2019
Yeah, I think we may need to go over it again. Like I knew it was one of the two, just wasn't sure which one. I know doing the chain out helps, but even then sometimes I get confused.
RaviJanuary 16, 2020
@Lucas, based on the information Ben gave us, we have a new term (U) in the conclusion. This means that for sure the missing premise will have that. P1: R - >not S P2: P3: T - >S
C: T - U
We need a chain that will push out T - >U. How can we do this? Well, let's start the chain with P3 (T - >S) since T is on the sufficient side of the conditional statement.
T - >S
Now, how can we chain this to the rest of the statements? Let's take the contrapositive of P1 (R - >not S), so now we have S - not R. We can add this to T - >S to get
T - >S - not R
Remember, we're trying to conclude T - >U. How can we get there now? We know we have to fill in the missing premise, and we know that U must appear. We have T on the sufficient side of the conditional chain already, so we need to add not R - >U to complete the chain.
T - >S - >not R - >U
This allows us to properly conclude the conclusion, which is T - >U
Hope this helps. Let us know if you'd like more clarification!
