implication Definition and 74 Threads

If p, then q. Suppose p is false but q is true. Why is it that the implication "If p, then q" is still true? For example, If x=2, then x + 3 = 5. Suppose x is NOT 2 (i.e. p is false), but x+3=5 (q is still true). Why is the implication "If x=2, then x + 3 = 5" still true? Is the...

Scenario 1: Imagine you are in an inertial reference frame and a planet is moving past you very quickly. A photon is coming towards you and will also pass the planet. The photon is not on a collision-course with you. Scenario 2: You are at rest relative to a planet and a photon is coming...

Hi, I'm struggling to find a constructive proof (through natural deduction) of the material implication replacement rule (i.e., that (a => b) <=> (~a \/ b). I believe the only possible way would be through contradiction, but I can't seem to get to it. Is it even possible? Thx.

Homework Statement Hi everyone, I need help on proving or disproving this: Please just show me how to do one of them, and I'd like to try to do the rest on my own. If I don't know then I will post more questions here.Homework Equations The Attempt at a Solution So far, I've interpreted this...

Both the logical implication and approaches use the same symbol. Have the two ever been famously confused? Is it implied that one or the other only be used in a specific context? logical p --> q approaches x --> positive infinity

I know the answer is many, some of them I already understand very well, time dilation etc, some other I might be able to grasp the idea (like light cone) and I will not be able to understand some others (i can't name it because i don't know what i don't know) I am a 2nd year physics major...

The truth table for A\Rightarrow B Means If A then B else Not B? But the truth table is supposedly looking like this: \begin{array}{ccc} A & B & A\Rightarrow B \\ T & T & T \\ T & F & F \\ F & T & T \\ F & F & T \end{array} Only problem I have is A=F and B=T? Why...

I'm not an expert in mathematical logic by far. But I understand that Godel's incompleteness theorem states that there can be some statements in an arithmatical system that are true but cannot be proven by that system. But that sounds like an implication. For part of the definition of an...

In logical implication (p implies q), if p is false, then no matter q is true or false, p implies q is true. But I think the negative of "p implies q" is "p implies not q", if so, if p is false, both "p implies q" and its negative are true, which is not possible. So is the negative of "p implies...

Hey everyone, I just thought of a mind-boggling "thought experiment": As a reminder, the formula for water pressure acting on an object due to weight is: (Water density)*(Acceleration of gravity)*(Depth of object underwater) Note that the shape of the container doesn't matter...

The other day someone gave me a puzzle. It was a geometry type puzzle but I was a able to reduce it to a set of pythagorean triads. Essentually the problem turned out to be equilvalent to the following. Find natural numbers a, b and c (each less than 42) such that {a, b, c} forms a...

Homework Statement All healthy food does not taste good. " Spinach is a healthy food. Duncan only want to eat tasty food. Duncan does not eat spinach. Hamburger is not a healthy food. Write all possible conclusion. I try to translate it into proposition with quantifier, such as t(x)=x is...

I have a problem which is best explained with an example: sqrt(A)=B => A=B^2 <=> B=-sqrt(A) or B=sqrt(A) Since A=B^2 <=> B=-sqrt(A) or B=sqrt(A) I should be able to reverse the order of this into B=-sqrt(A) or B=sqrt(A) <=> A=B^2 But if this is done in the first equation you...

This is a really basic question that I don't know why I'm not getting. So from my understanding, a=b is defined as a=>b and b=>a. So say a^2=c and a=c^(1/2) so which implies which? Say I start from a=c^(1/2) I square both sides and I get a^2=c. So a=c^(1/2) => a^2=c. But if I...

Hi all! I am currently preparing for an oral exam in quantum field theory and particle physics and I have some problems with the SU(3)-Hadron Multipletts and the relation to the Gell-Mann-Nishijima equation: First, for SU(2) Multipletts you take your Casimir-Operator J, some commuting...

Now suppose for simplicity that the galaxy,and that its physical diameter was w at the time it emitted the light.find the apparent angular size of the galaxy as it would be observed from Earth today. the answer given by Mr.Guth seems imply that the galaxy itself is also expanding and point out...

if s^{'}_{n} = s_n + b and S^{'}_{n} = S_n + b and s_n < A < S_n does that imply that s^{'}_{n} < A+b < S^{'}_{n} ? ahh why can't i delete, i think this is probably obvious the actual point of contention is if A is the only number between s_n and S_n is A+b the only number between...

So what we have so far is that any and all subsets are implied by a set. If there exist a set, then all the subsets within it are implied to exist also. This includes the elements of a set. The elements of a set are implied by the existence of a set. One of the most natural things to do with...

Just checking here. Propositional logic connectives like AND and OR have analogs or representations in set theory. For example, the logical connective AND is represented in set theory by intersection, an element of X AND Y is the element of the intersection of sets X and Y. And similarly, the...

Homework Statement C = (Ax)(EY) (p(X) -> p(Y)) D = (EX)(Ay) (p(X) -> p(Y)) Are C and D equivalent? Homework Equations Truth table for implication T T -> T T F -> F F T -> T F F -> T The Attempt at a Solution Well I believe C is true is all cases and is a tautology...

A chapter I am reading says that with "\frac{1}{x}=\frac{1}{2x+1}\Rightarrow2x+1=x", the \Rightarrowcannot be replaced by \Leftrightarrow, but if a = b, does not 1/a necessarily = 1/b? Is this a misprint or are they right? If they are right, could you illustrate this with an example please?

my post i really about discussing the difference that a mathematical representation does to physics. for example, let's take for example a system which can be be represented by quaternions and by complex numbers. if we can represent a physical theory by quaternions which aren't commutative...

Can someone try and explain it to me? I cannot understand the meaning of implication ( if p then q) from truth table p q p => q t t t t f f f t t f f t so it is if p is true then q is true or if p is false then q is false? then why if p is false and q...

HM...interesting What would you make of the following statement: If the following statement is true, then the preceding statement is false. Is the implication false? True?