Task $1$ Translate, Translate, For a Very Important Date $[18$ pts$]$ Translate these English statements into logic, making the atomic propositions as simple as possible and exposing as much of the logic via symbols as possible. a$)$ Define a set of at most four atomic propositions. Then, use them to translate $$If the area is low and wet, then Sitka Spruce are the most common spruce in the area. Otherwise, in high or dry territory, Engelmann Spruce are the most common spruce in the area.$$ b$)$ Define a set of at most four atomic propositions. Then, use those propositions to translate each of these sentences: i$)$ If the queue is empty, you can insert but not remove. ii$)$ If the queue is full, you can remove but not insert. iii$)$ If the queue is neither full nor empty, you can both insert and remove. c$)$ Define a set of at most four atomic propositions. Then, use them to translate each of these sentences: i$)$ Either your cat has fleas or your dog has fleas. ii$)$ If your dog has fleas and you administer flea medicine, then your dog is happy. But if your cat has fleas and you administer flea medicine, then your dog is not happy.