Statements into “Loglish”

1. Which of the following are correctly-written sentences of SL, and which are not? For that aren’t, explain why they are not. (/10) a. (U & C & ~L) b. ~O c. M~N d. ~(P ∨ Q) e. ((S ∨ (Q ≡ ~S)) & R)   2. Paraphrase each of the following statements into “Loglish,” and then symbolize them in SL. Indicate which letter you assign for each sentence you symbolize. (/10) a. Not all joggers are marathon runners. b. Either Clarence or Robert will vacation in Bermuda. c. If Carol will run in the Boston marathon, so will Albert. d. Both George and Emily will graduate with honours, or neither will. e. Phil will see the new Thor movie if and only if both Chris Hemsworth and Natalie Portman are in it.   3. Paraphrase each of the following statements into "Loglish," and then symbolize them in SL. Indicate which letter you assign for each sentence you symbolize. (/10) a. If Donna graduates with honours so will Fred, and if Bob graduates with honours so will Emily. b. Either George or Emily will graduate with honours, but they won’t both do so. c. The Red Sox have a good chance of winning the World Series if and only if the Mariners, the Angels, and the Twins all lose it. d. Felice will vacation in Bermuda if and only if Veronica does and Robert doesn’t, and Veronica will vacation in Bermuda if and only if Robert does and Clarence doesn’t. e. Neither Betty nor Eric like TV shows, but they do both like Bill Hader, and if he stars in Barry then they will both watch it.   4. Transform the following argument into an SL argument in standard form by first paraphrasing each sentence in “Loglish,” and then symbolizing them into SL sentences. Include a symbolization key indicating which letter you assign for each sentence you symbolize. (/20)