1. Translation into Logic (24 points) Translate these English statements into logical language, decomposing each sentence as much as possible into atomic propositions.

(a) [10 Points] Use the same atomic propositions to turn all of these sentences into logic. i) If the stack is empty, you can push but not pop, ii) If the stack is full, you can pop but not push. iii) If the stack is neither full nor empty, you can both push and pop.

(b) [6 Points] If we can develop cars that run on solar power or hydrogen power then we will not have a 3 degree rise in global temperatures this century and sea levels will rise less than 10 feet.

(c) [8 Points] Use the same atomic propositions to turn both of these sentences into logic. i) You either take the highway or surface streets. ii) If you take the highway and there is no accident you will arrive in time but if there is an accident you will arrive late unless you take surface streets.