A predicate logic sentence w is satisfiable if there exists some interpretation in which w is true. A predicate logic sentence is unsatisfiable (i.e., it is a contradiction ) if it is not satisfiable (in other words, there exists no interpretation in which it is true). It is valid if every interpretation is true.
We know that, P implies Q can be written as,
~P ∨ Q.
Therefore, the sentence becomes,
~P ∨ Q → ~P
Further solving,
~P ∨ Q → ~P
= ~(~P ∨ Q) ∨ ~P
= P ∧ ~Q ∨ ~P
= P ∨ ~P ∧ ~Q
= TRUE ∧ ~Q
= ~Q
Now, ~Q can either be true or false. Hence, the sentence is satisfiable.