When does p implies q noted as p---->q,

and when does p logically implies q noted as p====>q

solid examples would help.

in a mathematical proof we use logical implication or just simple implications

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- Aug 18th 2008, 01:52 PMtriclinothe difference between implication and a logical implication
When does p implies q noted as p---->q,

and when does p logically implies q noted as p====>q

solid examples would help.

in a mathematical proof we use logical implication or just simple implications - Aug 18th 2008, 02:30 PMPlato
**In my view there is absolutely no difference is the two expressions.**

Now, be warned that I am also sure the there is out there somewhere an author and textbook that will take great exception with my thinking that. For example, I recall reviewing a logic textbook in the 70’s in which the author took some five pages to argue that there are no such things as*propositions*. He maintained there are only*sentences*that are true or false. I think I recall his going so far as to say those who talk about*propositions*are just idealists and Platonists. - Aug 18th 2008, 04:27 PMtriclino
- Aug 18th 2008, 05:11 PMPlato
- Aug 19th 2008, 01:25 AMibnashraf
ok i was just browsing through some notes and came across the following. hope it helps ....

The truth of $\displaystyle p \rightarrow q$ is sometimes described by the expression "p is a sufficient condition for q" or "q is a necessary condition for p"

example:

p = "it is raining"

q = "there are clouds in the sky"

$\displaystyle p \rightarrow q$ is true

but $\displaystyle q \rightarrow p$ is false.

Given two compound propositions P and Q, we say that P logically implies Q, if Q has the truth value true whenever P has truth value true. we write $\displaystyle P \Rightarrow Q$ when this occurs.

Note that $\displaystyle P \Rightarrow Q$ iff ( $\displaystyle p \rightarrow q$ ) is a tautology.

That is, $\displaystyle P \Rightarrow Q \longleftrightarrow (p \rightarrow q)$ - Aug 19th 2008, 06:24 PMtriclino