(1) For the following statement, produce a gate diagram. (20 pts. each) (A nand B) implies (!B xor (B implies C)) (2) Turn the follow phrases into logical statements. Use the capitalized words as your variables. ( 10pts. each) (2.1) Either you can go to the MOVIES, or you can obey QUARANTINE (but you can't do both!) (2.2) If Charlie finds a WATCH, then he will not be LATE. (2.3) Steve doesn't have a CAT nor does he have a DOG, and Steve's not very SOCIAL. (2.4) If I get out to a RESTAURANT, then I'm expecting to have a nice MEAL or good SERVICE. (3) State the logical equivalences needed in order to turn one of these statements into the other. ( 20pts.) Statement 1: (!A or (!B and !C)) and (B or !B) Statement 2: (A nand (B or C)) (4) Determine if the following logical statement is valid via truth table: (20 pts.) A. Steve can exclusively either Study or Sleep. B. If Steve studies, then he'll Pass his Exam. Conclusion: If Steve Sleeps, then he'll NOT Pass his Exam