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this all revolves around the order of the words applies and only.
if the phrase was 'The Final Value Theorem only applies to systems with no right-half plane poles' then it would be false because there are also systems with no jw-axis poles and systems with no left half poles that it applies to.
if the phrase was 'The Final Value Theorem applies only to systems with no right-half plane poles' then its true because it is saying that the FVT and having right-half poles are mutually exclusive, which is true if what you've said about the FVT is true.
Can a JW Axis pole be considered to be on the RHP?
Your explanation seems pretty clear to me, so I'd see if other people in the class got hung up on the wording of this question as well and take it to the prof as a poorly worded question rather than an argument on semantics.
Likewise, if a system has any JW poles other than a single origin pole, the FVT does not apply.
That doesn't say which side the other poles are on. They could be RHP, LHP, or both.
that's my take...
Sorry, that was a miscommunication in my explanation. If a system has a RHP, it is excluded from FVT, even if it does have an origin pole (any RHP pole makes the system unstable, which means it does not have a final value). The FVT can only be applied to a system with an origin pole if it also has no RHP poles.
I think the analogy I'm going to give him is:
Let's say that a toll booth is installed on a highway, but only certain vehicles will have to pay the toll. All cars will pay the toll, and all trucks will be exempt from the toll. Most buses are also exempt from the toll, unless the bus has no passengers, in which case it has to pay the toll.
In this analogy, the toll represents the final value theorem. The cars are the LHP pole systems - the toll, or FVT, always applies to them. The trucks are RHP pole systems - if a vehicle is a truck, it is always excluded from the toll, just like a system with any RHP poles is always excluded from application of the FVT. The buses are jw-axis pole systems. For the most part, they are excluded from application of the toll (FVT), but there is a specific case in which the toll can be applied - when the bus has no passengers, or when there is a single pole on the origin.
So the equivalent statement is "the toll applies only to vehicles that are not trucks." This is true, because the toll is never levied from a truck. However, it does not imply that all non-trucks must pay the toll.
Am I just terrible with the English language because "the toll applies only to vehicles that are not trucks" at least to me means that every vehicle that isn't a truck pays the toll which is why you're example would be wrong and the professor is correct about the original question.
You might be able to get your points back, but if you do it won't be because you're right, but because the statement is ambiguous. Precisely because of the lack of clarity, you won't usually see the word "only" in a logical proposition, except as a part of "if and only if". The word "only" by itself doesn't have a well-defined meaning in logical terms, or it never did in any courses I took anyway.
I think you are correct. I would try to convince the professor by giving another example with the same sentance structure. For example:
"You can legally drive on public roads in Washington state only if you have a valid drivers license."
I would say that the above statement is true. It is true in spite of the fact that you might have a valid drivers license and still be unable to legally drive (for example, if you are drunk, or if you aren't wearing your glasses, etc.). If the statement had two crucial extra words:
"You can legally drive on public roads in Washington state if and only if you have a valid drivers license."
then it would be false.
Likewise, if the problem on the test had two crucial extra words:
"The Final Value Theorem applies to and only to systems with no right-half plane poles."
then the answer would be false. Those two crucial words were not present, so the answer is true.
Posts
that's my take...
if the phrase was 'The Final Value Theorem only applies to systems with no right-half plane poles' then it would be false because there are also systems with no jw-axis poles and systems with no left half poles that it applies to.
if the phrase was 'The Final Value Theorem applies only to systems with no right-half plane poles' then its true because it is saying that the FVT and having right-half poles are mutually exclusive, which is true if what you've said about the FVT is true.
Your explanation seems pretty clear to me, so I'd see if other people in the class got hung up on the wording of this question as well and take it to the prof as a poorly worded question rather than an argument on semantics.
Am I just terrible with the English language because "the toll applies only to vehicles that are not trucks" at least to me means that every vehicle that isn't a truck pays the toll which is why you're example would be wrong and the professor is correct about the original question.
"You can legally drive on public roads in Washington state only if you have a valid drivers license."
I would say that the above statement is true. It is true in spite of the fact that you might have a valid drivers license and still be unable to legally drive (for example, if you are drunk, or if you aren't wearing your glasses, etc.). If the statement had two crucial extra words:
"You can legally drive on public roads in Washington state if and only if you have a valid drivers license."
then it would be false.
Likewise, if the problem on the test had two crucial extra words:
"The Final Value Theorem applies to and only to systems with no right-half plane poles."
then the answer would be false. Those two crucial words were not present, so the answer is true.