I have a confusion regarding how to check whether a wff is satisfiable, unsatisfiable and valid.
As far as I understood, valid means the truth table must be a tautology, otherwise it is not a valid wff. For eg, p or (not p)
is valid since it is a tautology, whereas p and (not p)
is a contradiction. So it is not valid.
Unsatisfiable means the truth table is a contradiction. ie. A wff which is not valid is unsatisfiable. Eg. p and (not p)
Satisfiable can be a tautology or even if there is one True value in the truth table. Eg. p or (not p)
is tautology and not(p implies q)
has one True. So, they are satisfiable.
Am I correct about the terms? If not, please explain with simple examples like what I've used. Thanks in advance.
UPDATED:
Please check out [satisfiability][1] In that there is a definition about satisfiability which confuses me. It says, a formula 'A' is satisfiable if and only if 'not(A)' is not a tautology