Give an example of a truth-functional syllogism.
A truth-functional syllogism is an argument form where the conclusion is determined solely by the truth values of the premises. Let's consider the following example:
Premise 1: If it is raining, then the ground is wet.
Premise 2: It is raining.
Conclusion: Therefore, the ground is wet.
In this example, we have a simple truth-functional syllogism. Premise 1 states a conditional relationship between rain and the ground being wet. Premise 2 asserts that it is currently raining. Based on these premises, we can logically deduce the conclusion that the ground is wet.
To evaluate whether this argument is valid, we can apply the truth table method. Assign the values "true" or "false" to each premise and check if the conclusion holds true. In this case, when premise 1 is true and premise 2 is true, the conclusion is also true. Thus, this argument is valid.