1. Which of the following are sentences of SL (s), merely formulas (f), or neither (n). (Bear in mind that any sentence is also a formula. So write exactly one of s, f and n for each.) a) (^x)(Fxy>Gyy) b) (^x)Fx>~(%y)Gy c) Lx^y d) (x)Fxv >(y)Gxy 2. Symbolize each of the following using as interpretation: Universe of Discourse: everything Mx: x is male Fx: x is female Rx: x is a Republican Cx: x is a country Px: x is president of the US Lxy: x is the leader of y g: George W. Bush u: the US a) George W. Bush is male. b) There is a president of the US. c) All females are Republicans. d) Some Republicans are females. e) Some male Republican is leader of some country. f) No president is a Republican. g) Some male republican is the leader of every country. h) Every country has a Republican leader. 3. Using the interpretation (or symbolization key) given at the top of problem 2, determine and give the truth value of the sentences mentioned in a) through c) then use this information to say what you can about the validity of the argument of d). a) `~(^x)Rx´ is true? False? b) `(%x)Px&(%x)Rx´ is true? False? c) `(^x)(Rx>Px)´ is true? False? d) From your answers to a) to c) can you show that the following is valid or invalid? ~(^x)Rx (%x)Px&(%x)Rx _________________ (^x)(Rx>Px)

Derivations...