Wednesday, September 4, 2013
Assignment 2 - Question 11
Let D be the statement "The dollar is strong", Y the statement "The Yuan is strong" and T the statement "New US-China trade agreement signed". Express the main content of each of the following (fictitious) newspaper headlines in logical notation. (Note that logical notation captures truth, but not the many nuances and inferences of natural language.) How would you justify and defend your answers?
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a) D Λ Y
ReplyDeleteb) T Λ D Λ ¬ Y
c) ¬ (YΛ D)
I agree with these three.
DeleteHere are my thoughts for d and e:
ReplyDeleted) T Λ (D V Y)
e) ¬T Λ (D Λ Y)
Please correct! These are hard.
Francis,
DeleteFor d)Since both the dollar and yuan are weak I used
~D and ~Y and T
I had the same answer for e) as you
Here is my take on it:
ReplyDelete(a) D and Y
(b) T ^ ~Y ^ D
(c) (D and not Y) or (not D and Y) or (not D and not Y)
(d) T and (not D and not Y)
(3) not T and (D and Y)
Susan and Diane agree about d, and I see the sense in that since the statement is that it doesn't prevent a fall--implying that they both are weak. My initial thinking was that the headline about T didn't necessarily imply that D and Y were falling *at the moment.* I think that's too much of a stretch of interpretation, though, so T Λ ¬(D Λ Y) works for me.
DeleteBTW, you can cut and paste the symbols from someone else's reply to make the task of replying easier. Futzing with a new set of fonts and finding the appropriate set-symbols is a PITA. At least it was for me.
I agree about the cut-and-paste, Francis. I was replying on my work computer, where I have limited time to do that kind of thing. Of course, my home computer is even worse -- it is new and has the Evil Empire's Windows 8 installed. A great operating system for a tablet or phone, absolutely horrible for someone with a laptop who is used to working with a zillion apps running in the taskbar. (Math terms: ¬(Word Λ PDF) at the same time.
ReplyDeleteSo, how many people are using this blog? Is it as small a number as indicated by the responses, or are there multiple lurkers?
ReplyDeleteA good question, Francis. Although I advertised the creation of this blog on the "Over 40" board, I kept the blog open (anyone can post). Here are the statistics as of two minutes ago:
DeleteNumber of page views:
Today: 38
Yesterday: 100
All time: 727
Where the people are:
United States 636
Canada 25
Serbia 11
United Kingdom 9
Australia 8
Egypt 5
Romania 5
Pakistan 4
Germany 3
Israel 3
The browser used:
Chrome 228 (31%)
Safari 186 (25%)
IE 156 (21%)
Firefox 144 (19%)
Silk 8 (1%)
Safari 4 (<1%)
And statistics as posted on the class announcement page today:
Students
Total Students 46,107; Active Students Last Week 26,839
Now, that IS massive!
Thanks, Diane. When Dr. Devlin indicated in one of the vids that the class size was ~65K last time offered, I was gob-smacked (thank, those of you in the UK, for that lovely term). The fact that 46K signed up this time and ~27K were active last week amazes me.
DeleteIt's good to see the blog being read by others. I hope the viewers will join in. No matter what Marilyn vos Savant says (see my post in General Discussion), I think math is crucial to being well educated.
Francis, I am one of those mysterious lurkers. I imagine many of the over-40 group are working and have limited time to devote. I am retired and give almost 24/7 to this and I am still muddling and feeling challenged.
DeleteI just watched the video and saw I was being parenthetically defensive with my answers - but they were close on to what he had surmised. I had also for some reason considered T as a case within D and Y related to, instead of a separate entity...but I did not do that each time. I am using % as 'not/negation'.
ReplyDeletea.) D /\ Y (correct)
b.) (T %Y) /\ D (incorrect) if T is a separate entity I would not have thought this way.
c.) (D/\ %Y) V (%D /\ Y) (incorrect) : it is more elegant his way.
d.) I actually got the right answer T /\ (%d /\ %y) but extra parentheses (from programming, I guess)
e.) same as d with parentheses problem but it is correct format %T /\ (D /\Y)
In response to Francis: I will add that math is crucial to the exercise of some brains - wishful that would be all, but some cannot feel 'healthy' without it ;)