ASSIGNMENT 1. Translate the Seven Sentences below into Symbolic Logic.
For Conjunctions use the â€œ.â€ symbol.
For Disjunctions use the small case â€œvâ€.
For Conditionals use the â€œ>â€ symbol.
For Negations use the â€œ-â€œ symbol.
For Equivalences use the â€œ=â€ symbol.
1.) If I am living in America, I am Free. I am Free, so I must be living in America. (L=I am living in America, F=I am free)
2.) Fire causes smoke. There is fire. So, there must be smoke. (F=Fire, S=smoke)
3.) Either our lives happen out of coincidence or on purpose. Our lives do not happen out of coincidence. So, our lives must happen on purpose. (C=our lives are a coincidence, P=our lives have purpose)
4.) If Joe is a Communist, he rejects Capitalism. Joe is not a Communist. So he must not reject Capitalism (C=Joe is a Communist, R=Joe Rejects Capitalism)
5.) If Republicans were the same as conservatives, the two would share the same views on all important matters. But they do not. So, Republicans are not the same as conservatives. (R=Republicans are the same as conservatives, S=Republicans and conservatives share the same views on important matters)
6.) If I am an American, I believe in Democracy. If I believe in Democracy, I hold freedom dear. So, if I am an American, I hold freedom dear. (A=I am an American, D=I believe in Democracy, F=I hold freedom dear).
7.) If I am a Communist, I reject the idea of private property. If I am a Patriot, I defend our country. Either I am a Communist or a Patriot. So, either I reject the idea of private property or I defend our country. (C=I am a Communist, R=I reject private property, P=I am a Patriot, D=I defend our country).
ASSIGNMENT 2: Use the Comparative Method and tell whether the above arguments are
Valid or Invalid and name the argument form in each case.