Propositional Logic Questions: 1

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Propositional Logic Questions:

1. Symbolize the given argument, using symbolized simple propositions and the relevant truth functional connectives. Provide a complete key that indicates the variables you use to symbolize ordinary language simple propositions. Provide a complete truth table to discern whether the argument is valid or invalid. Your truth table should contain all the appropriate rows and columns. Explain what you see in your truth table that displays your answer. 
 

Either I will take a trip to Europe this summer or I will save my money and hang out with my old friend. If I do the latter, I will do a lot of "applesaucin'." So, if I don't take a trip to Europe this summer, I will do a lot of "applesaucin'.

 

2.  Symbolize the given argument, using symbolized simple propositions and the relevant truth functional connectives. Provide a complete key that indicates the variables you use to symbolize ordinary language simple propositions. Provide a complete truth table to discern whether the argument is valid or invalid. Your truth table should contain all the appropriate rows and columns. Explain what you see in your truth table that displays your answer. 
 

If the cube was soluble and it dissolved, then it was placed in liquid.
If the cube dissolved if and only if it was placed in liquid, then it was soluble.
Therefore, if the cube was soluble if and only if it dissolved, then it was placed in liquid

 

3.  Symbolize the four propositions contained in Molly Perry's philosophy, using symbolized simple propositions and the relevant truth functional connectives. Provide a key that indicates the variables you use to symbolize ordinary language simple propositions. Provide a complete truth table to obtain an answer to the questions about Molly's philosophy. Your truth table should
contain all the appropriate rows and columns. Be sure to show your work. Explain how your truth table indicates your answers. 

Molly Perry expresses her philosophy as follows:

"If the mind is identical to the brain, then personal freedom does not exist and humans are not responsible for their actions. If personal freedom does not exist, then the mind is identical
to the brain. Either humans are responsible for their actions or the mind is not identical to the brain. If personal freedom exists, then humans are responsible for their actions."

Is it possible that Molly's philosophy makes sense?

If so, what does it say about the mind, personal freedom and responsibility?