Logic Definition and 1000 Threads

Hi, First let's say you have an input vector and an output vector describing states. Let us use a binary number system, it doesn't really matter for mathematics. Say, I have an input vector V, components v_i. Now I would like to have an output vector W which can be of other dimension. The...

hi,, i m a bit confused in XNOR gate logic for MORE THAN 2 INPUTS.. is this logic correct "even function of 0's".. need help in this regard,thanks in advance.. :confused:

Although a physicist probably would just shake his head and point to the usual Hilbert space framework, it is nonetheless tempting for anyone dabbling in Mathematical Logic to see if any of the existing structures out of Model Theory could be appropriate for quantum physics concepts. The closest...

Hello, I can understand most boolean simplifications however I cannot grasp this one: (A+C+D)(A+C+'D)((A+'C+D)(A+'B) where the ' symbol represents a NOT. Without using Karnaugh maps can someone please tell me how to go about simplifying this expression ? Thank you kindly for any help.

Is there a simple way I can measure the propagation delay of my logic gates? For instance, is there a circuit I can build (using logic gates) to measure the propagation delay? What if I tried building a circuit whose output constantly oscillates? This would certainly prove that the...

Given: 1)it is not true that : 2>0 and 2+3 =7 2)if it is not true that 2>0 then 2 is less or equal to zero 3)if 2+3 =7 ,then 3+3 =8 4) but 3+3 is not equal to 8 Then prove: 2 is less or equal to zero

Hi This is a question from my self study of ch.2 of Alfred Tarski's Introduction to Logic Which of the following implications are true from the perspective of mathematical logic? a) If a number x (assuming x is an integer) is divisible by 2 or by 6, then it is divisible by 12 b) if 18 is...

Attached is a picture of IIL (integrated injection logic) cell. I understand the operation of the second (bottom-most) transistor, and analysis of digital circuits is adequate only understanding the operation of this transistor. I do not understand the operation of the transistor with...

Amount of Set Theory "Required" to Study Logic Hello, I have been self-studying set theory to try and get into logic. The book I bought is published by Dover (I love how cheap their books are) entitled Set Theory and Logic by Robert Stoll. I have gone over the basic set theory section...

This question is really getting on my nerves. It's 6i) from here: Right off the bat, it looks like they've thrown me a curveball. The fact that v does not occur free in \psi means that the Existential Hypothesis rule is going to need some care when applied. I've come up with two possible...

Hello I'm learning about proofs and in my book there's a sect. On mathematical induction. And I'm trying understand why this makes it true for all values. 1+3+5...2n-1=n^2 Suppose that the formula is known to be true for n=1, and suppose that as a result of assuming that it is true for n=k...

Homework Statement I need to simulate a AND/NAND gate with Emitter Coupled Logic. As I'm sure that most of you know, ECL is mostly used to make OR/NOR gates, so finding out how to make a NAND/AND gate is not as easy as it sounds. Homework Equations The Attempt at a Solution I...

Hello, I have a project that involves the coupling of a 12V Alternator with a small engine to power a loaded 12V battery. The gas engine is 1.4HP (1043.979Watts) coupled to a 40 Amp 12V alternator which is charging a 12V battery under a 35 Amp load. The way I see it, the 35 amp load...

Three scholars are riding in a railway car. The train passes through a tunnel for several minutes, and they are plunged into darkness. When they emerge, each of them sees that the faces of his coll~agues are black with the soot that flew in through the open window. They start laughing at each...

In an airplane there are 16 seats, 4 for the airplane crew (pilots) and 12 for travelers. I must write a logic function which is always one when the airplane crew is on their seats(4), how many people are in the airplane it doesn't matte (0-12)r. My 1st idea is: For each seat i define a variable...

Give a formal proof to show \forall x (0' + x' ) = (x . 0'') \vdash \exists x (x + x')= (x . x') I'm new to these, and this one looks like it should be easy. What I want to do is: 1). substitute x into where there are already x's. 2). Make the statement valid for all y 3). substitute y into...

Is it true that the following definitions of completeness are equivalent? \mbox{For theory } \Sigma \mbox{ and for any sentence } A. \mbox{ Either } \Sigma \vdash A \mbox{ or } \Sigma \vdash \lnot A and \mbox{ Either } A \in \Sigma \mbox{ or } (\lnot A) \in \Sigma. (The second clearly implies...

Does anyone honestly know what this is? I mean we use it in an argument, in the mathematical discipline every day. How can we tell something is non sense compared to logic, or if it is true and "correct" logic? What can we define to be logical, or a tautology? I think logic is a superb topic for...

Homework Statement Convert the logic circuit to an equivalent circuit constructed from 2-input NAND gates and NOT gates. http://imgur.com/EzOBdbv Homework Equations Pretty sure the boolean equation is: A & (~(~B+C)+~D + E) The Attempt at a Solution I know for sure that ~A + ~B = ~AB so I was...

Homework Statement The problem and its solution are attached. Homework Equations N/A The Attempt at a Solution All I think I know is that pins 7 and 14 are used for powering the integrated circuit because that's what I believe I read but, I don't fully understand what's going on. I...

Homework Statement The problem and its solution are attached. Homework Equations N/A The Attempt at a Solution I'm very confused about how output pulse trains work. I already checked online (including Wikipedia) so, could someone please give me an explanation of the absolute basics in...

If P→Q, and P is false but Q is true, then why is P→Q true? To me, it seems as though we shouldn't be able to do proceed because there isn't enough information. Same goes when P and Q are both false, how does that suggest P→Q is true?

I am currently looking at charlieplexing that can in theory cause me to be able to control eight 7 segment displays using 8 microcontroller pins, however in practice there is not enough current to drive all the displays. What I need is to increase the current drive from the microcontroller...

For those of you more into logical thinking, here are a few related problems I made up. They are not difficult by any means and are mostly meant to improve deductive skills, logic and proofwriting. Please be comfortable with the basic properties of the totient function as we'll use it as a...

So I'm working on two questions while learning C. The first question is, I need to create a program that prompts a user "Please enter an integer" and display whether the answer is odd or even. I'm using the logic that you can divide the input by 2, if the answer is a whole number it is even...

I am trying to begin with fuzzy logic, but this initial question is preventing me from moving any forward. It appears that fuzzy logic control is just an improvement over bang-bang control system. Like instead of doing bang-up , bang-down it does bang-up-hard, bang-up-small bang-down-small etc...

so I'm having problems with logic exercies especially when it asks you to prove long equations like when you just use simple integers and then prove that like asqtb/a > 2 and such, ifind them very difficuly idk if it's just me ,i don't find other lessons that hard ...

I wonder how can I make the logic gate read 0V when it is open? For instance, the AND logic gate. If one of its input pin has 5V supply, and the other don't have, the output signal given to me is 5V. How can I make it 0V? Well, theoretically, it should be 0V, but in reality, it appears that...

I have problem in building my mini-project as stated in the topic.I am actually confused how the robot will follow a signal like micro wave or radio wave, this kind of wave just spreads and the robot will get confused where to go.I just want opinion what shall i do that the robot will come to...

Homework Statement There exists a function f. Assume that you are given f's CNF representation and f's DNF representation. The CNF representation has some number of clauses, and each clause has 3 literals. The DNF representation has some number of terms where each term has 3 literals. The...

Homework Statement We can't use anything else, and just have to make a logic circuit (either OR, AND or NOT) with just this material. We can use less or more diodes but I have only 5. Homework Equations The Attempt at a Solution I tried setting it up like doides but no help at...

The problem: (Note: the correct answer is bolded throughout) A basketball is launched with an initial speed of 8 m/s at a 45 degree angle from the horizontal. The ball enters the basket in 0.96 seconds. What is the distance x and y? Just ignore the distance x, I know it's simply the product...

Hello all. Just a quick question about logical operations gears can preform. I know if you have a large gear turn a small gear, the center of the small gear will spin faster than the large. But are there any other logic operations that gears can preform? Thank you for viewing.

According to the truth tables in my computer architecture text, P → Q is false if P is true and Q false; and true otherwise. I cannot understand why it is "true" otherwise. For example, if P and Q are both true, P → Q is also true, but this makes no sense to me. Perhaps Q is true for...

(I am not sure if this is the right section for this). This question probably is extremely trivial and silly, but I haven't been able to find the answer to it despite going through quite a bit of The Internet. So, it appears that each Quantum Logic Gate corresponds to a matrix. Ones that...

I viewed previous tests on the internet. There are logic gate problems in a test. What subject do this logic gates problems belong to? What book do you recommend for understatnding this subject?

Basically, is a digital circuit the same as a logic circuit? I.e. Is a logic circuit another name for a digital circuit because am i right in thinking that all digital circuits are a set of logic functions e.g. Logic gates which follow the rules of boolean algebra?

Hi, I've got another answer I'd like checked. I'm pretty sure it works out, but I want to be certain. Homework Statement Write a sentence in everyday English that properly communicates the negation of each statement. "Some differentiable functions are bounded." Homework Equations The...

Hi all, Just a few question about FOL logic. What is the difference between terms and atoms, I read lot's of differents definitions, then when I think that I've understood, I find an exemple where both are used without any difference (for ordering by instance). An another question is : What...

This is not a homework problem but in fact a solved example question. The full question text is below with answers and my reasoning for them. Could someone please explain the reasoning behind part (c). A coffee shop sells 5 types of coffee (latte, mocha, espresso, cappuccino and iced...

Homework Statement Complete the truth table for the following http://forum.allaboutcircuits.com/image_cache/httpwww.freeimagehosting.netuploadsd537e2dd9a.jpg Homework Equations JK Flip Flop Characteristic Table D Flip Flop Characteristic Table The Attempt at a Solution I...

Recently, in the Scientific American blog http://blogs.scientificamerican.com/observations/2012/11/29/person-of-the-year-nomination-for-higgs-boson-riddled-with-errors/?WT_mc_id=SA_CAT_physics_20121130 the author criticizes Time Magazine for its science reporting, which of course is nothing...

First of all, I wasn't quite sure in which (sub)forum to post this, so if it doesn't quite fit, feel free to move it. I'm having a very hard time solving this one (or even seeing if it's logically consistent), and any help would be very much appreciated. Homework Statement Give a formal proof...

Uncapable of working through the tensors of the EFE's or visualizing the concepts upon which they are based as expressed in that manner, I have begun reverse engineering GR in an attempt to determine the basic concepts upon which it is based to find the foundation of its mathematical logic and...

Homework Statement http://media.newschoolers.com/uploads/images/17/00/58/56/03/585603.png Homework Equations None The Attempt at a Solution I have tried just messing around with them, and I have tried to turn this table into a "boolean" expression. I have no idea how I would begin to solve...

Homework Statement I have a weird boolean algebra expression for which I need to build a circuit using solely the NAND gates. There are 4 inputs A,B,C,D. From the truth table (I do not know how else to approach this question other than constructing the truth table and then trying to fit the...

Actually, I have several questions: 1) Why are axiom schemas the way they are? What do they represent? I know that infinitely many axioms can be written using the axiom schema form. However, what's the formal definition of axioms in predicate calculus? I've heard that the formal definition of...

This exercise is from my Discrete Mathematics course and it requires a step by step solution, backed up by logical equivalences or deductions made based on the rules of logic. 5 students, Oliver, Simon, Peter, Bob and Christie all seniors at Harvard, come from one of the following cities...

Homework Statement I was having a casual chat with one of my professors and he presented me with a problem that after 4 hours of attempting I believe is unsolvable. the set up is pretty simple. you have 3 inputs x,y,z that go into a system, the output is ~x,~y,~z. However you are only allowed...