PART B. (10 marks) Translate each of the following short arguments into propositional logic and test for validity using truth-tables, the method of assigning values, or by constructing a truth-tree. 11. If cryptocurrencies are a viable alternative to fiat currency then central banks will take notice. But if central banks take notice, then the government will move to regulate cryptocurrencies. Any viable alternative to fiat currency must be independent of state control, but if the government moves to regulate cryptocurrency then cryptocurrency is not independent of state control. Consequently, cryptocurrency is not a viable alternative to fiat currency. i. Invalid. ii. Valid. (2 marks) 12. If Stephanie is an influencer then her meal at the new caf will be on the house. But Stephanie is not an influencer if she doesn't have any influence. Now, if she is an influencer, then Stephanie has a lot of followers and her posts attract a lot of likes. But none of this is sufficient for having any influence. So, even if Stephanie has a lot of followers and her posts attract a lot of likes, Stephanie will still have to pay for her meal. i. Invalid. ii. Valid. (2 marks) 13. John will not get a seat at the front of class unless he arrives on time. The instructor will call roll right at the beginning of class provided she herself is not late or has forgotten her notes. If she's not on time and John does get a seat at the front, he'll be able to finish his homework. So, if the instructor neither forgets her notes or is late, then John will get his homework done. i. Invalid. ii. Valid. (2 marks) PART B. (10 marks) Translate each of the following short arguments into propositional logic and test for validity using truth-tables, the method of assigning values, or by constructing a truth-tree. 11. If cryptocurrencies are a viable alternative to fiat currency then central banks will take notice. But if central banks take notice, then the government will move to regulate cryptocurrencies. Any viable alternative to fiat currency must be independent of state control, but if the government moves to regulate cryptocurrency then cryptocurrency is not independent of state control. Consequently, cryptocurrency is not a viable alternative to fiat currency. i. Invalid. ii. Valid. (2 marks) 12. If Stephanie is an influencer then her meal at the new caf will be on the house. But Stephanie is not an influencer if she doesn't have any influence. Now, if she is an influencer, then Stephanie has a lot of followers and her posts attract a lot of likes. But none of this is sufficient for having any influence. So, even if Stephanie has a lot of followers and her posts attract a lot of likes, Stephanie will still have to pay for her meal. i. Invalid. ii. Valid. (2 marks) 13. John will not get a seat at the front of class unless he arrives on time. The instructor will call roll right at the beginning of class provided she herself is not late or has forgotten her notes. If she's not on time and John does get a seat at the front, he'll be able to finish his homework. So, if the instructor neither forgets her notes or is late, then John will get his homework done. i. Invalid. ii. Valid. (2 marks)
