Truth Table determine statement

Question

( S ∨ M) ∨ (∼ M ⊃ S)

Determine if this statement is

1. Tautologous
2. Contingent
3. Self - Contradictory

Answer 1

This statement is *contingent*—it is neither a tautology (i.e., a logical truth) nor a self-contradiction. The best way to see this is to make a truth table for the statement. On the line where the atomic statements S and M are both false, the overall statement will come out false, too. On all other lines the overall statement comes out true. Because the statement comes out false on some lines (namely, the line where S and M are both false) and true on others, this means it is contingent. (Feel free to ask me for help with constructing truth tables!)