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### 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 ...
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### 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 &...
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### 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 ...
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### 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 ...
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### 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 $(\sim p \lor q)$. ...
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### 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, ...
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### Equivalence of $a \rightarrow b$ and $\lnot a \vee b$ [closed]

Is there a proof for the logical equivalence of $a \rightarrow b$ and $\lnot a \vee b$?
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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 $q$ ...
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{...
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### 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 ...
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"...
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 $44$ ...