956 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?

1 Answer

Best answer
5 votes
5 votes

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

Related questions

1 votes
1 votes
0 answers
1
1 votes
1 votes
1 answer
2
srestha asked May 31, 2019
835 views
The notation $\exists ! x P(x)$ denotes the proposition “there exists a unique $x$ such that $P(x)$ is true”. Give the truth values of the following statements : I)${...
4 votes
4 votes
4 answers
3
Gaurab Ghosh asked May 28, 2016
2,114 views
Is the assertion "This statement is false" a proposition?