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u/let_me_count_the_way · 4 pointsr/HomeworkHelp

What this expressions says

First of all let's specify that the domain over which these statements operate is the set of all people say.
Let us give the two place predicate P(x,y) a concrete meaning. Let us say that P(x,y) signifies the relation x loves y.

This allows us to translate the statement:
∀x∀yP(x,y) -> ∀xP(x,x)

What does ∀x∀yP(x,y) mean?

This is saying that For all x, it is the case that For all y, x loves y.
So you can interpret it as saying something like everyone loves everyone.

What does ∀xP(x,x) mean?

This is saying that For all x it is the case that x loves x. So you can interpret this as saying something like everyone loves themselves.

So the statement is basically saying:
Given that it is the case that Everyone loves Everyone, this implies that everyone loves themselves.
This translation gives us the impression that the statement is true. But how to prove it?

Proof by contradiction

We can prove this statement with a technique called proof by contradiction. That is, let us assume that the conclusion is false, and show that this leads to a contradiction, which implies that the conclusion must be true.

So let's assume:
∀x∀yP(x,y) -> not ∀xP(x,x)

not ∀xP(x,x) is equivalent to ∃x not P(x,x).
In words this means It is not the case that For all x P(x,x) is true, is equivalent to saying there exists x such P(x,x) is false.

So let's instantiate this expression with something from the domain, let's call it a. Basically let's pick a person for whom we are saying a loves a is false.

not P(a,a)

Using the fact that ∀x∀yP(x,y) we can show a contradiction exists.

Let's instantiate the expression with the object a we have used previously (as a For all statement applies to all objects by definition) ∀x∀yP(x,y)

This happens in two stages:

First we instantiate y
∀xP(x,a)

Then we instantiate x
P(a,a)

The statements P(a,a) and not P(a,a) are contradictory, therefore we have shown that the statement:

∀x∀yP(x,y) -> not ∀xP(x,x) leads to a contradiction, which implies that
∀x∀yP(x,y) -> ∀xP(x,x) is true.

Hopefully that makes sense.

Recommended Resources

Wilfred Hodges - Logic

Peter Smith - An Introduction to Formal Logic

Chiswell and Hodges - Mathematical Logic

Velleman - How to Prove It

Solow - How to Read and Do Proofs

Chartand, Polimeni and Zhang - Mathematical Proofs: A Transition to Advanced Mathematics

u/Alphonse_Mocha · 1 pointr/HomeworkHelp

No problem--I'm happy to help! If you get the chance (but I certainly understand a heavy work load), the book [But Is It Art?] (http://www.amazon.com/But-Is-It-Art-Introduction/dp/0192853678) is a really good introduction to a lot of critical theory that you will run into when dealing with 20th century art. Also, I don't think you can really use it as a true source for your paper, but I would also recommend [Postmodernism for Beginners] (http://www.amazon.com/Postmodernism-For-Beginners-Jim-Powell/dp/1934389099). We used it in an undergrad seminar when I was just starting to learn theory, and it was absolutely invaluable--very, very easy to read, and you really get a good overview of the major ideas and philosophers in Postmodernism. Good Luck!

u/FunWithCthulhu3 · 2 pointsr/HomeworkHelp

I think that's a fair assessment of 'the Absurd'. There isn't really a wrong answer here! In this game it's all about interpretation and supporting yourself logically and coherently. My suggestion to you then, is to take a look at The Myth of Sysiphus (and the [sparknotes won't you here hurt either] (http://www.sparknotes.com/philosophy/sisyphus/summary/)). Find yourself a breakdown of Camus' philosophy somewhere that you can understand. This is sprawling, complicated stuff, and no one in their right mind would expect someone in high school to write a comprehensive paper covering all of Camus' philosophy from source texts. Solomon's 'Existentialism' really is gold. I tried to find a pdf online for you, but it doesn't seem to exist. Since you seem to have an interest in the topic, I'd suggest picking this up at some point (maybe a birthday or Xmas gift?). Solomon also has a short little paperback called 'Introducing The Existentialists' which is worth picking up. Any more questions, ask away! Good luck!

u/Cosmic_Charlie · 1 pointr/HomeworkHelp

Two books that might help:

Odd Arne Westad, The Global Cold War Excellent analysis of US and USSR moves in smaller countries. Definitely gets into what I think you're looking for.

John Gaddis, We Now Know Gaddis is a bit heavy on the self-congratulations here, but this book is really good. Not quite as on point as Westad for your interest, but should still be helpful.

u/capcom1116 · 1 pointr/HomeworkHelp

This is an excellent book I've used from high school to college now. Find a guide like this, if you can, to help you learn how to find these things in the text.

Giving you any more specific information would be akin to doing the assignment for you, I'm sorry to say.

u/[deleted] · 1 pointr/HomeworkHelp

if u want to read a fun book - check out "DNA" by James Watson.

he explains a lot of concepts in biology in easy terms. and its interesting.

http://www.amazon.com/DNA-Secret-James-D-Watson/dp/0099451840

u/FirelordPhoenix · 3 pointsr/HomeworkHelp

You could write about memory championships and how everyone can train their memory for numbers, cards and faces.

EDIT: This book was a really interesting read on the topic.

u/chevybow · 1 pointr/HomeworkHelp

Polio


http://en.wikipedia.org/wiki/David_Oshinsky


It was the first thing I searched and it seems to fit your criteria.

u/blueboybob · 1 pointr/HomeworkHelp

halliday and resnick for general physics

1 - goldstein

2 - griffith

3 -

4 - griffith or jackson

u/book_moth · 1 pointr/HomeworkHelp

Read [The Children's Blizzard by David Laskin] (http://www.amazon.com/The-Childrens-Blizzard-David-Laskin/dp/0060520760)

or look at the wikipedia page about the same storm, the blizzard of 1888

We've done a lot to mitigate the damage from blizzards already by giving people a heads up that a storm is coming.

What eventually happened was the US government realized the need for weather forecasting.

u/reickmey · 1 pointr/HomeworkHelp

The air pressure provided is just a force over an area. For now, forget how the air pressure acts on the steel tube since the forces are almost negligible. The air pressure acts on the rectangular sign, which has a large surface area, (lets assume) uniformly. With a pressure and an area we can say a single force is applied at the center of the sign. That force is acting on the sign's center of mass, as it's positioned in the picture, which is (lets assume) rigidly attached to the the steel tube. The center of mass of the sign is 1.25m away from the center of the steel tube. This system will apply what is called a moment on the steel tube...also known as a torque. That 1.25m distance would be known as the moment arm. Closed cross sections, specifically circular cross sections, are good at resisting moments applied in this direction. One thing to also note is the force at the center of the sign also applies a moment, with a moment arm from the center of the sign to the ground which is 4.5m. This is a called a bending moment when a force is applied in this direction. When designing such a structure, as an engineer, you will need to be conservative and assume both moments will occur at the same time and the same location. So, apply both moments at the base of the steel tube, where it meets the ground. This will be the most critically loaded location on the structure. Read about Statics and Mohr's Circle which you will learn about in mechanics of materials. Pick-up a used copy of 'Mechanics of Materials'. There are a bunch of cheap listings here on Amazon. You should be able to understand how to solve that problem fairly quickly skimming that book.