Logic Definition and 1000 Threads

This from Alonzo Church's Mathematical Logic, been stuck on it for a week =(. Homework Statement 14.3 Present a Formal Proof: p \Rightarrow (q \Rightarrow r) \Rightarrow ((p \Rightarrow q) \Rightarrow r)Homework Equations The Attempt at a Solution A truth table has shown that the previous...

I have this challenge to do but can't seem to be able to understand it completely! I also have test right now and can't concentrate. Please help this poor soul! It will be appreciated! The first question is:Let F ∈ PROP. Let (h)F be defined by the number of parentheses in the formula F. a)...

What is the mean of " Effective logic inversion " ? Because I can't understand this qustion, " Describe briefly why there is an Effective logic inversion between logic level from a TTL IC and the LED load it drives? "

Homework Statement Let |A| denote the weight function in this way: |=>|=|⋁|=|⋀|=|<=>|=+1 | ┐|=0 |p|=|r|=|s|=-1 Now I need to show that one statement to be logic statement the sum of all symbols need to be -1, and the sum of the symbols in every series, starting from A is non-negative (i.e...

I know this is probably in the wrong board, but. I'v just been looking into some Boolean algebra to convert truth tables into a set of logic gates representing a circuit. If i were attempting to represent a certain truth table, but i was limited to ONLY using NAND gates. (their the only...

I have been trying to familiarize myself with a particular system of first-order logic with identity, in which the process of substitution is achieved by replacing, one at a time, one occurrence of a variable with a term. (see axiom schemes 6) and 7)). I want to use these axioms to prove the...

1. Mark as true or false. The implication "If P, then Q " is equivalent to: a) P is necessary for Q b) Q is sufficient for P c) P is sufficient for Q d) Q is necessary for P e) P only if Q f) Q only if P It seems like there's missing something..If P is what? I don't get this...

I've been reading articles on logic gates and What I want to do before I get to school is familiarize myself with what individual components are used in making those individual gates on say a breadboard.I keep searching for it on the web but it just gives me the schematic symbols and not what...

Dear All, Having trouble with a seemingly simple logic truth table. Are these answers correct? \begin{tabular}{| c | c | c | c | c | c |} \hline p & q & r & (p \vee q)\wedge(q \vee r) & (\neg p \wedge q) \vee ( p \wedge \neg r) & p \rightarrow q \rightarrow r\\ \hline T & T & T...

Dear All, Having trouble with a seemingly simple logic truth table. Are these answers correct? \begin{tabular}{| c | c | c | c | c | c |} \hline p & q & r & (p \vee q)\wedge(q \vee r) & (\neg p \wedge q) \vee ( p \wedge \neg r) & p \rightarrow q \rightarrow r\\ \hline T & T & T & T & F...

Working on a homework for a general astronomy class. Just want to make sure I'm not being inaccurate. Please let me know if I goofed something up. Thanks! RQ7: The word “apparent” in “apparent visual magnitude” is used to denote its dependence on viewing distance. These numbers refer to...

M_{12}=\frac{N_2\phi _{12}}{I_1} i need to remmeber it but i can't see the logic of the formula ??

Hi guys, I have searched the forums but I don't think what I really would like to ask is covered :D. I would really like to find a book for self study on introductory Mathematical Logic, I am not really looking for anything covering Sets Or Number theory (unless of course the text is really...

The book which i read for improving my logic sense~ There is a theorem called REPLACEMENT .. ( P \rightarrow Q ) \vee \neg ( P \rightarrow Q) where (P\rightarrow Q) is the second occurence of ( P \rightarrow Q) But what if the replace the second occurrence with \neg P\vee Q! And i try...

Does anyone know if there is a relationship between the requirement in Quantum Computing that logic gates be reversible and the requirement in Quantum Mechanics that observables have to be self-adjoint?

I have the following book: https://www.amazon.com/dp/0072401893/?tag=pfamazon01-20 I'm currently going over symbolization and truth-functional connectives. I have a question considering a material conditional paraphrasing. Of course, you cannot state this backwards. If he applied for the...

This is VBA Excel: Here is what I am trying to do. I have a MathML file saved as a .txt file. It is simialr to XML. From the XML file, we have a bunch of text that looks something like: <mname>Salad</mname><mrow>xyz</mrow> I would ultimately like to have an array whose elements are the...

I've got quite an unusual hobby project and so far, after couple of nights googling, I haven't found software that would fit the bill. I've got the truth table representing what I'd like to do and can minimize & map it to gates using Logic Friday. The problem is, I don't have NOR or NAND...

Edited Q1 + solution attempts Homework Statement Q1: Represent the following using only NAND gates, and only NOR gates Q1a) A.B + ~(A.C).~(B+C) Q1b) (A XOR B) + ~(A XOR B).(B + C) Q2: Design a combinational logic circuit that converts a 4 bit sign magnitude representation of a number...

Sorry to have two threads up at the top of the Science Book Discussion forum, but I couldn't find a thread for this. I'm interested in learning some mathematical logic. Here are the books I'm considering, please tell me what you think of them or suggest better alternatives. Mathematical Logic...

Jun3-03, 03:02 PM C0mmie "... logic is not an attribute of the universe, but instead is our means of understanding the universe, while the universe itself has nothing to do with logic. For expample, imagine a person who for the first time in his life is exposed to Heisenberg's...

Curry's paradox can be used to (dis)prove the riemann hypothesis and string theory, and even prove the (non)existence of God... no, actually, Curry's paradox IS God. :biggrin: Just kidding... I am now (speaking somewhat hyperbolically) freaked out. Does Curry's paradox go like this (try "1 =...

Hello all I cannot find a simple explanation of the meaning of this axiom, probably because it is considered so obvioius that it needs no explanation. Can anyone explain in words. {a}\rightarrow{({b}\rightarrow{a})} Thanks. Matheinste.

Homework Statement 1.Assume the language has equality and a two-place predicate symbol. Given two structures (N;<) and (R;<), find a sentence true in one structure and false in the other. Can these two structures be elementarily equivalent? Can they be isomorphic? Why or why not? 2.The...

Homework Statement Using only AND and NAND gates, design a circuit in which 4 switches must all be turned on before a switch in another circuit turns off. i think half the reason i don't understand may be the wording of his question, i know the tables but i am not sure how the logic gates...

How is this definition ( I made up): Logic is the deductive (as opposed to empirical) science of all possible worlds.

Homework Statement You ask your friend if the football is on 9pm or 10pm. He sometimes tells the truth and sometimes doesn't. What should you ask him so that you will be certain which time the football will be on? The Attempt at a Solution ASK: Is it true that 'You are telling the truth...

I'm not squeezing this into my degree (Physics), but I'd like to buy a good Logic textbook online or whatever. Thanks.

Hi, I've been trying to work out the formula for the sum for the full adder logic, however have come across a gap which I don't know how to fill. S = (¬A.¬B.C) + (¬A.B.¬C) + (A.¬B.¬C) + (A.B.C) S = ¬A.(¬B.C + B.¬C) + A.(¬B.¬C) S = ¬A.(B \oplus C) + A.( [SIZE="1"]do not know what to do at this...

What would be such a book which is modern and clear with good excercises and solutions?

Homework Statement Prove or disprove: "If you can prove ( y \wedge \neg c ) \rightarrow Contradiction , then y \rightarrow c must be right."Homework Equations My teacher used the sign \wedge , instead of \vee , like: "If ( a \wedge b \wedge \neg c ) \rightarrow Contradiction , then...

how could i express using only the operator NOR (in logic) the rest of operation NOT(x) AND(x,y) OR(x,y) that is how i could prove that the Logic operator NOR is functionally complete

Hi, all. Wikipedia says: In logic, the law of the excluded middle states that the propositional calculus formula "P ∨ ¬P" ("P or not-P") can be deduced from the calculus under investigation. It is one of the defining properties of classical systems of logic. However, some systems of logic...

Homework Statement I am supposed to prove that if you have a puzzle 8 in this configuration A B C D E F H G I have to prove that no matter how many moves you make (as you would a normal puzzle moving one of the adjacent...

Helloo every one, here is my qusetion: Design acircuit that has three inputs a,b,c and has three outputs a' ,b', c' . your circuit can only have two inverters and any number of AND and OR gates if some 1 could help me i'd appreciate it.

Can I use this logic? Homework Statement I'm wondering if I can use this kind of logic to solve: \sum\frac{(n+1)^n}{n^{(n+1)}} Converges or diverges The Attempt at a Solution \frac{(n+1)^n}{n^{(n+1)}} \geq \frac{(n)^n}{n^{(n+1)}} And \frac{(n)^n}{n^{(n+1)}} = n ...

Homework Statement I'm studying logic gates and trying to create my first one. Homework Equations 3. In a TV programme, the panel votes on new performers. The panel consists of a Chairman (C) and three others (X, Y and Z) who each press a button to register their vote. The SUCCESS light is...

Hi. So a classic logic puzzle goes like this: At noon the hour, minute, and second hands coincide. In about one hour and five minutes the minute and hour hands will coincide again. What is the exact time (to the millisecond) when this occurs. (Assume that the clock hands move continuously.) If...

Can someone tell me what order someone should learn physics until they can say that they totally know physics (please don't write something like you can never learn everything in physics) Thanks!

I`m studying Engineering -not mathematics-, so what is a good book to start with?

Hi, I am helping my children with a computer game based on Logic and Reasoning. The player has to solve different puzzles as the game progresses. I am struggling with a matching puzzle where the player has to form a string of the game characters based on their traits. Please see the attached...

Homework Statement (p -> q) has an unambiguous meaning both in logic and in natural language. The DeMorgans laws tell us what is meant by the negation of a conjunction or the negation of a disjunction, but what is the negation of a conditional such as p -> q? Use the rules of logic to produce...

http://img21.imageshack.us/img21/3070/11650282.th.gif on the limsup case each time we take out the biggest member of the sequence . so it goes to the smallest memeber how its supposed to be the supremum of the limits

I have been trying to study first-order logic to have a sound basis on mathematical language. The main target is to have a clear path: I start with first-order logic (the language), then I go and study set theory, which is in fact a series of axioms (ie, a series of statements of the language)...

W_1 and W_ 2 are subspaces of V of inner product V. prove that if W_1\subseteq W_2 then W_1^\perp \supseteq W_2^\perp the proof is: we take v\epsilon W_1 so <v,w>=0 for every w\epsilon W_1^\perp and because W_2^\perp \subseteq W_1^\perp (i can't see why the "viven expression is...

Is it equivalent? ( \forall x \in S \forall y P(x) ) <=> \neg ( \exists x \in S^{c} \exists y \neg P(x) ) Attempt at solution I think it should be ( \forall x \in S \forall y P(x) ) <=> \neg ( \exists x \in S \exists y \neg P(x) ) The diiference to the above statement is S^{c}.

Homework Statement \forall x \in S <-> \exists x \not \in S The Attempt at a Solution The statement is clearly false. I will try to show that by the proof of contradiction. Let P: \forall x \in S and Q: \exists x \not\in S The negation of Q is negQ: \forall x \not\in S and the negation...

Homework Statement Let u and v be two nonzero vectors in R^2. If there is no c E R such that u = cv, show that {u, Bv} is a basis of R^2 and that R^2 is a direct sum of the subspaces generated by U = <u> and V = <v> respectively. Homework Equations Clearly, u and v are linearly...

Hi, I'm trying to build a digital circuit that will perform one of three logic functions on a set of three inputs A B C based on the input value of a counter that counts mod-3 (00, 01, 10). I can use basic chips such as mux, demux, 555 timer, logical chips Thanks

1. Negate the following statements (i): \forallx\inR \existsy\inR such that x+y=0 (ii): introduction: Each of us got, let's say, 20 bags of green apples. Actual Statement: At least one of us (each) found at least one red apple in at least one bag (each). (Each person and each one of it's...