Consider two well-formed formulas in propositional logic
$F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$
Which one of the following statements is correct?
$F_1: P \Rightarrow \neg P\equiv\neg P\vee \neg P\equiv\neg P$
When we put $P\equiv T$ it will $F$
and When we put $P\equiv F$ it will $T$
It is called contingency.
Always false called contradiction or unsatisfiable
Always true called valid or tautology
At least one true called satisfiable.
$F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)\equiv\neg P\vee P\equiv T$(Always true)
F1: $P\to \neg P$
$=\neg P\wedge \neg P$
$=\neg P.$ can be true when P is false ( Atleast one T hence satisfiable)
F2: $ (P\to \neg P)\wedge(\neg P\to P)$
$=\neg P \vee (P\vee P)$
$=\neg P \vee P$
what is invalid or Faulty in terms of propositional Logic ?
Falsy means always false or contradiction.
Invalid means at least one false
@ bhanu kumar 1
Read the entire comment and answer, you will understand better.
"A valid (true for every set of values) formula is always satisfiable (true for at least one value) , but a satisfiable formula may or may not be valid".
as F1 is not valid but satisfiable,
and F2 is valid(which implicitly means is satisfiable too).
therefore OPTION A is the complete solution, but OPTION D is not.