In logic, a sentence is satisfiable if it has at least one interpretation that makes it true. A sentence is valid if it is true in all interpretations. A sentence is contradictory, or unsatisfiable, if it is not satisfiable, meaning no interpretation makes it true.
Let us look at the sentence. The given sentence is as follows:
S: (P ∨ Q) ⇒ (P & Q)
Let us draw truth table for both sides of the sentence.
P | Q | (P ∨ Q) | (P & Q) |
T | T | T | T |
T | F | T | F |
F | T | T | F |
F | F | F | F |
As we can see that the LHS implies RHS only in two cases. This means that the statement is true in only two cases and false in two cases. Since the sentence is true in at least one interpretation, but not true in all interpretations, this sentence is SATISFIABLE.