in Mathematical Logic
937 views
3 votes
3 votes
“Not every satisfiable logic is valid”

 Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$

or

$2)\sim \left ( \forall S(x)\vee V(x) \right )$

Among $1)$ and $2)$, which one is correct? and why?
in Mathematical Logic
by
937 views

3 Comments

I think 2 because the expression of 2 can be simplified as --> there exist(S(x)) ∧ ~V(x))

where as 1 states--> ~ (if a logic is satisfiable then it is valid)..this means if a logic is satisfiable then it is not valid..but this is not the case, it may be valid may not be valid  

0
0
Isn't the same example given in Rosen? Before asking please see reference books - you'll learn more rather than seeing someone's comment/answer. Only when you have genuine doubts or complex stuffs which are not in standard books, you should ask -- that's how people become GATE toppers.
3
3
Actually, we blindly know, $\rightarrow$ work with $\forall$, but no meaning behind it. I want to know, if there is really any meaning behind this.
0
0

1 Answer

5 votes
5 votes
Best answer

Not  = ~

Every = $\forall$

logic = $x$

Satisfiable = $S( )$

Valid = $V()$


“Not every satisfiable logic is valid”   ( It means that the underline statement is not true)

= Not (every satisfiable logic is valid)

=Not( For all logic if a logic is satisfiable then it will be valid)

= $\sim ( \forall(x) S(x) \rightarrow V(x) )$

selected by

4 Comments

Please check now.
0
0

why "if....then"??

"is" represents by $"\rightarrow" ??$

if I say like this

"every logic satisfiable AND valid"

then where is error?

0
0

"every logic satisfiable AND valid" will not hold.

Because valid is depending on satisfiable.

AND means no dependency.

 

 

2
2

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true