For all of the following five arguments, translate the premises and conclusion into Propositional Logic using the capital letters given in each problem. Next, choose any one of problems 2-5 to construct a long truth table for, and analyze the argument for validity. You can construct a truth table by inserting a table into a Microsoft Word document (from the INSERT option in Word, choose “table.” You will then have an opportunity to choose how many rows and columns you would like your table to be.) Is the argument valid or invalid? If valid, identify the rows in the table that demonstrate validity by showing that in all cases where all premises are true, the conclusion is always, also true. If the argument is invalid, identify the row in your table where the premises are true and conclusion false.
Finally, for problem 1 construct an abbreviated truth table as described in both the module overview and section 7.4 of the textbook (rules for this are summarized on page 367 of your text).
To summarize, you are translating all five problems, then constructing a long truth table for one of problems 2-5, and, last, constructing an abbreviated table for problem 1.
Being undetermined is a necessary but not a sufficient condition for human behavior's being free. The laws of subatomic physics are statistical only if human behavior is not determined. And the laws of subatomic physics are statistical. It follows that human behavior is free. (D: Human behavior is determined; F: Human behavior is free; L: The laws of subatomic physics are statistical)
Given that nuclear energy is needed if and only if solar energy cannot be harnessed, nuclear energy is not needed. For solar energy can be harnessed provided that funds are available; and funds are available. (N: Nuclear energy is needed; S: Solar energy can be harnessed; F: Funds are available)
Erik attains Valhalla given that he is valiant. And Erik is depressed assuming that he is not valiant. Furthermore, Erik fails to attain Valhalla only if he is not depressed. Thus, Erik is depressed. (E: Erik attains Valhalla V: Erik is valiant; D: Erik is depressed)
Not all living things are able to feel pain. For all living things are able to feel pain only if all living things have nervous systems. But not all living things have nervous systems given that plants do not have nervous systems. And plants do not have nervous systems. (L: All living things are able to feel pain; N: All living things have nervous systems; P: Plants have nervous systems)
There are necessary truths. If there are no necessary truths, then there are no necessary connections between premises and conclusions. But there are no valid arguments if there are no necessary connections between premises and conclusions and there are valid arguments. (N: There are necessary truths; C: There are necessary connections between premises and conclusions; V: There are valid arguments)
