As we can observe, the rules in a conditional statement say that the only instance wherein the conditional statement becomes false is when the antecedent is true and the consequent false. Let us take this statement:
If the airship Albatros has a powerful weapon, then it could destroy objects on the ground. (S, T)
Now, the first row in the truth table above states that p is true and q is true. So, obviously, p ⊃ q is true. This is because, if it is true that “The airship Albatros has a powerful weapon,” then it must also be true that “It could destroy objects on the ground.”
The second row states that p is true and q is false. So, p ⊃ q must be false. This is because if it is true that “The airship Albatros has a powerful weapon” then it should necessarily follow that “It could destroy objects on the ground.” However, it is stated that q is false, that is, the “It could not destroy objects on the ground”; therefore, the conditional statement is false. For sure, it is not sound to conclude that the airship Albatros does not have the capability to destroy objects on the ground given that it has a powerful weapon. Hence, again, the conditional statement is false.
The third row states that p is false and q is true. If this is the case, then p ⊃ q is true. This is because if it is not true that “The airship Albatros has a powerful weapon”, then it does not necessarily follow that it could not destroy objects on the ground. In fact, even if the airship Albatros does not have a powerful weapon, it is still possible for the airship Albatros to destroy objects on the ground.
Finally, the last row in the truth table above states that p is false and q is false. If this is the case, then p ⊃ q is true. This is because, based on the example above, it states that “The airship Albatros does not have a powerful weapon” and that “it could not destroy objects on the ground.” Hence, obviously, the conditional statement is true.
