There are 5 predicate calculus questions I've been working on, I think I've correctly solved the first four, except the last one I have no idea where I'm going with. I'll present my work and the questions below. Any help would be appreciated. The task is to translate the sentences in the language of predicate calculus using the 3 symbols provided:  R(X) : ”X is rich”  X ' Y : ”X equals Y”  B : ”Bill Gates”  a) Someone besides Bill Gates is rich.  ANSWER: ∃x(R(x)∧¬(x=B))  b) Bill Gates alone is rich.  ANSWER: ∀x(R(B)∧(¬(x=B)=>¬R(x)))  c) At least two people are rich.  ANSWER: ∃x(∃y(R(x)∧R(y)))  d) Exactly one person is rich.  ANSWER: ∃x(∀y(R(x)∧(¬(x=y)=>¬R(y))))  e) Exactly two persons are rich.  ANSWER: No clue!
I've been doing some practice questions in the textbook for an upcoming predicate calculus lecture and I think I've managed to get A and B (possibly C) correct but I am clueless on how I can manage D and E.   For A I got: ∃x(R(x)∧¬B)  For B I got: ∀x(¬R(x)∧B)  For C I got: ∃x(R(x)∧(x=y))   - Not sure if this is even remotely correct    R(X) : ”X is rich”  X = Y : ”X equals Y”  B : ”Bill Gates”  a) Someone besides Bill Gates is rich.  b) Bill Gates alone is rich.  c) At least two people are rich.  d) Exactly one person is rich.  e) Exactly two persons are rich.  The universe of discourse is the set of all people.
Auto size image to page size in InDesign I've got an InDesign document with 100 A4 pages.   I've got 100 assets (a mixture of .jpg and .pdf files) and I want to place 1 per page. If an image is not the proportion of the A4 page I would like to get it as big as it can be on the page before it hits into the margin. Ex. if it's a portrait image it should be as large as it can be before hits the top/bottom margin. If it's a landscape image it should be as large as it can be before hits the left/right margin.   At the moment I'm dragging each file across and resizing them manually. Is it possible just drop them on the page and get them auto resized ? Why isn't there a continuously differentiable surjection from $I \to I \times I$? I was asked this question recently in an interview. Why can't there be a a continuously differentiable map $f \colon I \to I \times I$, which is also surjective? In contrast to just continuous, where we have examples of space filling curves.  I have one proof which is direct via Sard's theorem. But the statement seems simple enough to have a proof using at most implicit (and inverse) function theorem. Is Bran able to have children after his fall? The thing that made me ask this question was that most of Stark family are dead and Bran is now the "heir" to Winterfell. So I guess he should have children to succeed him, otherwise the Stark line will end. (I'm assuming Arya will not come back to Westeros and Rickon's fate is sealed, though I could be wrong.) I don't remember reading anything about it. Does anyone know the name of travel posters from the 1930s? Is there a name for this design style - use of flat colours for dimension and shading - that was so prevalent in UK travel posters of the 1930s? How does the formation of a solar system not break the second law of thermodynamics? Please forgive: I am a layman when it comes to physics and cosmology, and have tried finding an answer to this that I can understand, with no luck.  As I understand it, the solar system evolved from a massive molecular cloud. To me, this seems to break the second law of thermodynamics, as I think it suggests order from disorder.  I know there must be something wrong with my logic, but am really stuck.  Can anyone explain this one in layman's terms?  (Posting to both "Astronomy" and "Physics", as it seems to overlap these subjects) Dynamic pivot: sum of sales per month My table is like this:  Sitecode    Month  Amount --------    -----  ------ XX          Jan     1000 XX          Jan     3000 XX          Apr     3000 XX          Apr     1000   What I want is, to show the result something like this:  Sitecode    MonthJAN   MonthAPR --------    --------   -------- XX          4000       4000 Add air resistance to projectile motion I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals.  This is what I have so far:  If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, a_x = 0, a_y = -9.8$, and time will be 0,1,2,3... and so on.  Using these equations on every second you can find the plot will be a bell shaped with the highest point being ~ 325 m at about 600 seconds:   $$ x = x0 + (v_{0x})t + 1/2((a_x)t^2) $$ $$ y = y0 + (v_{0y})t + 1/2((a_y)t^2) $$  Usually in physics, we are taught in perfect condition with no air resistance. But what if there was air resistance? How would it affect this problem? How can i add it to my calculations and see what the difference is? Where can I get more favourable exchange rate, in general?changing baht to Canadian dollars in Thailand or Canada or make a bank transfer to my Canadian account JUnit @Test expected annotation not working From the :   -exec command ;     There are unavoidable security problems     surrounding use of the -exec action; you should use the     -execdir option instead.  -execdir command {} +     Like -exec, but the specified command is run from the     subdirectory containing the matched file, which is not     normally the directory in which you started find.  This a much     more secure method for invoking commands, as it avoids race     conditions during resolution of the paths to the matched     files.    What does this mean? Why are there race conditions with running it from the starting directory? And how are these security risks? Let $x, y$ and $z$ be real numbers such that $x^2+ y^2+ z^2= 1$. Find the   maximum and minimum values of $2x + 3y + z$ .       How can I able to solve the problem? Thanks for your help. Probability that a quadratic polynomial with random coefficients has real roots The following is a homework question for which I am asking guidance.     Let $A$, $B$, $C$ be independent random variables uniformly distributed between $(0,1)$. What is the probability that the polynomial $Ax^2 + Bx + C$ has real roots?   That means I need $P(B^2 -4AC \geq 0$). I've tried calling $X=B^2 -4AC$ and finding $1-F_X(0)$, where $F$ is the cumulative distribution function.  I have two problems with this approach. First, I'm having trouble determining the product of two uniform random variables. We haven't been taught anything like this in class, and couldn't find anything like it on Sheldon Ross' Introduction to Probability Models.  Second, this strategy just seems wrong, because it involves so many steps and subjects we haven't seen in class. Even if I calculate the product of $A$ and $C$, I'll still have to square $B$, multiply $AC$ by four and then subtract those results. It's too much for a homework question. I'm hoping there might be an easier way. I read through all the related answers, but they do not apply to Ubuntu 14.04.  I have no .gnome2 folder and no Passwords and Encryption keys item in the system settings. I tried to crawl through every possible menu, but I could not find out how to do it.  The popup usually pops out when I start Chromium. Impossible to hide navigation bars in Safari iOS 7 for iPhone/iPod touch How to get the key for a given object from an NSMutableDictionary? Maximum area of isosceles triangle with perimeter 6 cm This morning, I read Wikipedia's informal definition of a limit:     Informally, a function f assigns an output $f(x)$ to every input $x$. The   function has a limit $L$ at an input $p$ if $f(x)$ is "close" to $L$ whenever   $x$ is "close" to $p$. In other words, $f(x)$ becomes closer and closer to $L$   as $x$ moves closer and closer to $p$.   To me that sounds like something that might be better described as a 'target'.  If I take a simple function, say one that only multiplies the input by $2$; and if my limit is $10$ at an input $5$: then I've described something that seems to match the elements contained in Wikipedia's definition. I don't believe that that's right. To me it looks like an elementary-algebra problem ($2p = 10$). To make it more calculusy, I could graph the function's output when I use inputs other than $p$, but that really wouldn't give me anything but an illustration of the fact that one's answer moves farther from the right answer as it becomes more wrong (go figure).   So limits are important; what I've just described is trivial. I do not understand them. I know calculus is often used for solving real-world challenges, and that limits are an important element of calculus, so I assume there must be some simple real-world examples of what it is that limits describe.   What is a simple example of a limit in the real world?  Thank you  -Hal. Convert a string representation of a hex dump to a byte array using Java? I am looking for a way to convert a long string (from a dump), that represents hex values into a byte array.  I couldn't have phrased it better than the person that posted .  But to keep it original, I'll phrase it my own way: suppose I have a string "00A0BF" that I would like interpreted as the  byte[] {0x00,0xA0,0xBf}   what should I do?  I am a Java novice and ended up using BigInteger and watching out for leading hex zeros. But I think it is ugly and I am sure I am missing something simple. The title says it all.  If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right?  So my son posed me an interesting question today: since light travels as fast as anything can go, what if I shined light when moving in a car?  How should I answer his question? Bound for the correlation of three random variables