((~ P & ~ Q) This is not a sentence, as it contains an unmatched parenthesis. (P rightarrow rightarrow Q) This is not a sentence, as no sentence can have two occurrences of 'rightarrow' or any other connective save the negation sign in a row. (P Q & R) This is not a sentence because it does not have enough parentheses. Determine, for each of the following, whether it is a sentence of our language. If it is not, briefly note why it is not. (We will not, for the purposes of exercises of this sort, be dropping the outer -most pair of parentheses.) 1. ((~ ~ P & Q) Q & R) 2. ((P doubleheadarrow Q) doubleheadarrow (R doubleheadarrow ~S)) 3. ~ ~ ((~ P rightarrow Q) R) 4. ((P R)) doubleheadarrow S) 5. ((((P rightarrow Q) rightarrow R) rightarrow (S R)) doubleheadarrow ~ B) 6. (~ P rightarrow ((Q R) rightarrow S) doubleheadarrow W) 7. (((~ S doubleheadarrow Q) & R) rightarrow ~ (R ~ Q)) 8. (S rightarrow (~ PQ rightarrow S)) 9. ((S rightarrow ((((W & P) (Q ~ R)) (A & B)) rightarrow C) & D) rightarrow R) 3. (~ S rightarrow (((W & P (Q ~ R)) (A & B)) rightarrow C) & D) rightarrow R)