Logic Definition and 1000 Threads

To me, there is no doubt that logic cannot be constructed if it isn't initiated by a set of unprovable 'rules', axioms, to be more precise. For example, I can't prove that a statement is either true or false under any circumstances, but I do assume this is consistently true - if a statement is...

[SOLVED] can u make "if A>=B then output=1 Else output=0" using these logic gates? Homework Statement this is not quite a homework problem. I am designing a device and I need to use A>=B comparator. The challenge is I need to do this using only NAND, AND, NOR, OR and ExclusiveOR gates...

If I have P l- Q in FOL and P is closed, can I infer l- P -> Q. IIRC, this is valid as long as P is closed, but my memory is a little hazy. Is that how it works?

I need to understand how diode-resistor gates work. I've read a lot about what's supposed to happen based on inputs, but I need to see some numbers & analysis to understand what's going on. Where do you start in terms of trying to analyze the following AND gate...

Homework Statement Using basic gates and/or building blocks, design a logic circuit that takes in a 4 bit input and will compute the number of 1s in the input. Homework Equations The Attempt at a Solution I have no idea where to start can anyone help please.

Homework Statement Use logic to write the negation of the sentence: All participants of this course are IT majors and are Math majors (be careful, use basic logic laws) Homework Equations DeMorgan's Law The Attempt at a Solution Letting P(x) be Participants who are IT majors...

Can anyone tell me if the universal quantifier distributes over material conditionals in standard first order logic? Does (v)(Mv → Pv) imply {v)Mv -> (v)Pv? Does the implication work the other way too? Thanks.

Never mind there, I screwed up my logic flow

One of the following general laws is true, the other false. Prove the true one. Find a counter example to the other.(We must do this in writing out each statement, no truth tables or anything. (a) If X implies Y, then the disjunction of X or Y is equivalent to X. (b) If X implies Y, then the...

When I first heard about the fuzzy logic, some guys told me that it would replace all "classical mathematics", being superior to it, but scientists are unfortunately reluctant to accept it yet. I immediately concluded, that fuzzy logic would be pseudo science. I later learned, that fuzzy...

"Horses have heads" Symbolic Logic I was given this sentence to represent in first-order predicate calculus. The formula must use the following terms--horse, has, head--where: "horse" represents "x is a horse" "has" represents "x has a head" "head" represents "x is a head" Are these...

1. 11010101 / 11011 2. code each one of the deximal numbers by weight ( 6, 4, 2, -3 ) i don't know what the meen but some how i am sopposed to code using them 3. code the number 729 in excess3 code the number 729 in BCD code the number 729 in 2421 code i lack the theoretical knowledge to...

Homework Statement Richard is either a knight or a knave. Knights always tell the truth, and only the truth; knaves always tell falsehoods, and only falsehoods. Someone asks, "Are you a knight?" He replies, "If I am a knight, then I'll eat my hat." a) Must Richard eat his hat? b) Set this up...

So my teacher said that when proving something, I can't start out with what I'm trying to prove. But what if it is an "if this than that proof" For example, If A(squared)=A, then I-A=(I-A)inverse Well, I started using what I'm trying to prove by multiplying both sides by I-A I get...

im just starting to write proofs and it's going well but some things aren't immediately obvious to me. for example it is not immediately obvious to me why \forall_i ~ p_i \vee q_i \Leftrightarrow (\forall_i p_i ) \vee (\forall_i q_i) isn't a tautology and it wasn't immediately obvious...

Perchance someone here has some background in Philosophy, specifically symbolic logic? For the life of me I can't figure out the following: A v D (~B ^ ~C) = D B => ~(C=> A) ~B What I have so far is this: 1| A v D ......P 2| (~B ^ ~C) = D ....P 3| B => ~(C =>A) ...P 4| |B ......A...

what are the fundamental symbols in logic? maybe this is a vague question but that's cause i don't know anything about logic. are they \neg \wedge \vee? do we define the material implication in terms of these symbols? basically I'm having trouble understanding the paradoxical nature of...

Sorry if my title wasn't the best, dosen't know the english termonolgy Anyway i get diffrent result based on how i solve "pvq->r" the result vary if i solve this as (pVq)->r or pV(q->r). You can see me trying to solve this in the picture which i have attaced, below...

hi, could someone explain to me why the sentence - There are exactly two purple mushrooms is represented in FOL like this: (Ex)(Ey) mushroom(x) ^ purple(x) ^ mushroom(y) ^ purple(y) ^ ~(x=y) ^ (Az) (mushroom(z) ^ purple(z)) => ((x=z) v (y=z)) especially the last part i have problem with...

Hi, Really struggling with this logic problem, would be very grateful to anyone willing to help A v D (~B ^ ~C) <==> D B ==> ~(C ==> A) --------------------- ~B Thanks in advance Hayden Kee

http://www.headcook.co.uk/lodge-logic-dutch-oven-1025-p-2069.html?source=webgains&siteid=7963 Is this a good one? it looks way to big for cooking for one, but if i cook a batch of chili may be it will last all week?

[SOLVED] Logic gates problem...Need to check if my answers are correct.. Homework Statement http://img132.imageshack.us/img132/8899/19367959nt9.jpg Homework Equations The Attempt at a Solution http://img220.imageshack.us/img220/2338/answerslo5.jpg Now I wasn't sure how...

design the 2-bit mod-5 multiplication/division module using only basic logic gates. the number 0 is often ignored. Thus, in your design, the following 2-bit number representation is used: 00-->1, 01--> 2, 10-->3 and 11-->4. examples of mod-5 multiplication: 4 × 2 ≡ 3 (mod 5), 3 × 3...

I don't get why do we use Flip Flops for Finite State Machines? Can anyone explain? -Thankyou

What do they mean by saying that " If the clock frequency is 45MHz and we use 50MHz then the circuit will not work". I am confused :rolleyes: I don't understand the timing analysis in digital logic. Please help me out -Thanks

Is logic the answer to everthing? If it is, then how can it explain our existence, because logically we are not supposed to exist (in mind or matter). Logically you cannot get something from nothing. So can logic answer every question?

Mathematical Logic: "For all" and "There exists" I need to show that \vdash (\forall x)(A \rightarrow (B \equiv C)) \rightarrow ((\forall x)(A \rightarrow B) \equiv (\forall x)(A \rightarrow C)) My question to you, how does the (\forall x) affect this equation? If they weren't there, I...

Physics "logic" puzzles1 1. The battery output voltage, the bottle volume, the clock time, and the measure of weight all have something in common. Are they represented by: one number (I think this is the answer) more than one number 2. Water is shooting out of the end of a pipe. The end of...

I'm studying for my logic final and I can't seem to find an answer for this practice problem: (Using < as proper subset since I don't have the right type) T_1 < T_2 < T_3... be a strictly increasing sequence of satisfiable L-Theories. a) Show that the union of T_n is satisfiable (over...

I have a design issue. I've programmed a CPLD so that it controls whether a MIC can activate or not. There are 8 MICs. A MIC is allowed to activate if there are no opens nor shorts on its lines. Each MIC has 4 wires (red, black, white, green). The red and black wires are for the...

[SOLVED] digital logic design i want to simplify this function using four-variable map: F(w,x,y,z) = \sum(0,1,2,4,5,7,11,15) , the map contains one "1" at the upper right corner. my question is how can i take this 1 in a group? or what can i do with it?

The question asks you to prove A v C This is what I have. Everything is correct until the last question, #11 1. A V C 2. ~BvC 3.(new subproof) B 4. (new subproof ~B 5. contradiction contradiction intro 4,3 (end subproof from 4-5) 6. ~BvC V Intro 2 (end subproof from 3-6) 7...

[SOLVED] Boolean Logic - Multiple simple questions My professor, he's a good, witty guy. He wasn't satisfied with other textbooks, so he decided to write his own. Since it's not published yet, we get a free pdf version of it, downloadable. Sadly, despite how good of a person he seems to...

Hello, My name is Joe and I am a junior in high school. I am taking AP Calculus right now along with a basic physics class. I am very, very interested in the special and general theories of relativity, but I want to know the exact logic behind it. Right now, I don't really understand any of...

[b]1. How do you prove, using SD, that ((A>B)>A)>A? [b]3. I tried to first assume (A>B)>A. Then I made a sub-derivation, assuming ~A. In this sub-derivation, I need to derive a contradiction. How?

Can anyone verify if this logic has truth! Homework Statement My friend and I were having a chat about a friend that got injured on a water slide. He started to explain the physics of her body and its movement on a water slide and not being a physicist I want to see if someone can verify...

I've been thinking about if logic is meaningful and if so, what makes logic meaningful. Or more precisely, what makes the assertion that logic is meaningless meaningless. Do you require logic to question the validity of logic or attempt to establish its invalidity (because otherwise words...

I have a couple of homework problems that I can't get, hopefully one of you enlightened ones can help me. I have to give proofs of these valid arguments using only the 8 rules of inference (M.P. etc.), and 10 replacement rules(D.N. etc.) : (1) 1.(A>E)>C 2.C>~C /A...

If classical logic is inconsistent then so is classical mathematics. A. x=y -> (Fx <-> Fy). This is an axiom of first order logic and it is a theorem of second order logic. (Leibnitz's Law) A is a theorem of Principia Mathematica, *13.15. 1. x=y -> ([](x=x) <-> [](x=y)). therefore...

Homework Statement What subsets of the real line R are definable in (R;<)? What subsets of the plan R x R are definable in (R:<)? The Attempt at a Solution R and the empty set are the only definable subsets of (R;<) since: x to x+1 Is an automorphism and changes all subsets...

hi ^^ Draw the logic diagram of the following expression. The diagram should correspond directly to the equation. Assume that the complements of the inputs are not available: a . XYZ + X’Y’ + X’Z’. b . B(A’C’+AC) + D’(A+B’C) what does it mean ? do i have to draw the inverter? or not...

Homework Statement Draw the schematic circuit diagram that implements the following expression using as few basic gates as possible (AND, OR, NOT, XOR, NAND, NOR). The prime denotes the complement: f = w^\prime z^\prime + w^\prime xy + wx^\prime z + wxyz The Attempt at a Solution From the...

[SOLVED] Propositional logic Discrete Mathematics Homework Statement Assuming atleast one of the following statements is true, which one is it? why? a. Exactly one of these statements is true b. Exactly two of these statements are true c. Exactly three of these statements are true d...

Homework Statement A speed skater moving across frictionless ice at 8m/s hits a 5m patch of ice. She slows steadily then continues at 6m/s. What is her acceleration on the rough ice? Homework Equations Not sure The Attempt at a Solution 6m/s - 8m/s = -2m/s * 1/5m = 1/10 s...

one of my cousins asked me what the mathematical logic/mathematical explanation are behind the definitions of scalar product and cross product. he wants to know why the definitions are set like the way they are. i just want to make sure from you guys before i answer him. i think that there are...

Is an assertion that could be true but isn't always considered to be false or just lacking information?

Base conversion -- the LOGIC and INTUITION behind it... for example, converting from base 10 to 2, a systematic way is to divide the number by 2's successively and keep track of the remainder. the remainder coefficients represent the binary number. Now why does this work is beyond me but I...

Homework Statement Prove or give a counterexample to each statement. (S ∩ T) ∪ U = S ∩ (T ∪ U) The Attempt at a Solution If I proved by the contrapositive S (T ∩ U) ≠ (S ∩ T) ∪ U where would I go from there. How do I find the contrapositive with the unions and...

After much thinking I am trying to get a help from the board. Sorry for being naïve and thank you in advance for your answers. Suppose you have to arrays made up of zeros and ones a=(1,1,0,1,0,0) b=(1,0,0,1,1,0) and a logic relationship to compare the elements of the two arrays in a...

I am looking for excellent mathematical logic books that start from the beginning and go to the (what we think is) the end. Hopefully something with lots of editions so I can pick up a 2nd edition for 3 bucks on Amazon used. Ideas?