Linked Questions

4
votes
2answers
833 views

What's the sense in “Implies” logic? [duplicate]

Possible Duplicate: In classical logic, why is$ (p\Rightarrow q)$ True if both p and q are False? How to interpret material conditional and explain it to freshmen? We're told that ...
26
votes
10answers
6k views

Assumed True until proven False. The Curious Case of the Vacuous Truth

Given two statements, $P$ and $Q$, and the logical connective, $\implies$, the truth table for $P \implies Q$ is: $$\begin{array}{ c | c || c | } P & Q & P\Rightarrow Q \\ \hline \text T &...
9
votes
9answers
17k views

The meaning of Implication in Logic

How do I remember Implication Logic $(P \to Q)$ in simple English? I read some sentence like If $P$ then $Q$. $P$ only if $Q$. $Q$ if $P$. But I am unable to correlate these sentences with the ...
36
votes
1answer
15k views

What's the difference between material implication and logical implication?

When I read the definitions of material and logical implications, they seem to me pretty much equivalent. Could someone give me an example illustrating the difference? (BTW, I have no problem with ...
7
votes
6answers
8k views

Help to understand material implication [closed]

This question comes from from my algebra paper: $(p \rightarrow q)$ is logically equivalent to ... (then four options are given). The module states that the correct option is $(\sim p \lor q)$. ...
12
votes
5answers
5k views

Intuition of implication in propositional logic

So, in all the books on propositional logic, I feel unsatisfied with the "intuition" about the meaning of the implication connective. I completely understand how the mechanics work via truth tables, ...
7
votes
5answers
1k views

Equivalence of $a \rightarrow b$ and $\lnot a \vee b$ [closed]

Is there a proof for the logical equivalence of $a \rightarrow b$ and $\lnot a \vee b$?
5
votes
6answers
4k views

Tautology, Contradiction, or a satisfiable equation? Confusion about implication.

I'm having some trouble with a homework question. I have the following $ P \rightarrow \neg P$ This looks like a contradiction to me. This should never be true! Yet, if I transform it using $p \...
4
votes
4answers
3k views

Why do we use “If p,then q” instead of “Not p or q”?

I read almost all posts on material implication and vacuous truths on the site. I understood that it was introduced for mathematical convienience use and it does not have to perfectly align with our ...
3
votes
3answers
585 views

Implications and Ordinary language

I studied propositional logic, and everyday I see applications of what I learned on the internet, in mathematical books and miscelaneous resources. One particular case is sentences in the form $...
3
votes
4answers
141 views

truth value of “if…then…”

From the truth table, when both $p$ and $q$ are true, then "if $p$ then $q$" is true. However, this is a little weird as "if $p$ then $q$" is used to show the relationship between $p$ and $q$. If $q$ ...
2
votes
4answers
534 views

Justification of truth table of conditional statement if $p$ then $q$

I have gone through various sites but i can't understand the justification for the truth table of "If $p$ then $q$". Is it accepted by the mathematicians without any proof or justification? \begin{...
0
votes
1answer
352 views

On the truth-value of implication connective

As I have come to understand, in classical logic, the implication statement turns out to be true if the premise is false. It seems to be a little counter-intuitive, as it seems to me that the truth ...
1
vote
2answers
100 views

Representing sentences as propostional logic formula

I need to translate the following sentence: Whenever the alarm sounds the fan must be on and the building empty into a logical proposition. So I defined variable as follow: $p$ = "The alarm sounds"...
0
votes
2answers
69 views

About an implication in logic or mathematics.

The following is a question in an entrance examination of a Japanese university. A quadrilateral $ABCD$ is inscribed in a circle with a radius of $65/8$. The perimeter of this quadrilateral is $44$ ...

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