Part A: Using the constant (letter) assignments immediately below, display the pattern of each of the following four arguments, ignoring any minor variations in tense or mood. Be sure to put the arguments in standard form (numbering the premises and conclusion, putting the conclusion at the bottom with a line between it and the premises). Assess each argument for validity. If it is valid, name the pattern.
P= I go to Barcelona.
Q= The Canadian dollar is worth less than the euro.
R= I have money left over when I get home.
S= I go hiking in the Pyrenees.
1. I'll go to Barcelona only if I go hiking in the Pyrenees. So, I'm going hiking in the Pyrenees since I am definitely going to Barcelona.
2. I'll go to Barcelona if I go hiking in the Pyrenees. So, I'm going hiking in the Pyrenees since I am definitely going to Barcelona.
3. The Canadian dollar is worth less than the euro, since either it is worth less than the euro or I'll have money left over when I get home, but I will be broke when I get home.
4. I'm going hiking in the Pyrenees unless the Canadian dollar is worth less than the euro. And I'm going to Barcelona only if the Canadian dollar is not worth less than the euro. So, if I go to Barcelona, I'll go hiking in the Pyrenees. [Scroll down for Part B]
Part B: Construct an original example, in English in standard form, of each of the following. If it is not possible to do so, say why. Be sure to use premises and conclusions the truth value of which it is reasonable for you to believe that your marker knows. You do not need to use constants, but you might find that helpful. (If you use them, be sure to state explicitly what they represent!) Do not use any examples from class (and, please, don't use the Internet-that won't help you learn).
1. A valid argument with a false conclusion.
2. An invalid argument with a true conclusion.
3. A valid argument with a true conclusion.
4. An invalid argument with a false conclusion.