Determine which of the following are propositions and their truth values: a) New York is the United States Capital. b) Where is Central Park? c) 5x y 22 d) 48-21 14 e) Open the door 2. Let p and q be the propositions p: I will finish project. q : I will go to the movies. r: I will go to dinner Write the following propositions using P and q variables and logical connectives: a) I will finish project and I will go to the movies. b) I will not finish project. c) If I finish project, then I will go to the movies. d) If I don't finish project, then I will not go to the tennis tournament. e) IfI don't finish project, then I will go to the movies or dinner. f) I will go to the movies and dinner, iff and only if I finish project. 3. Let p, q, and r be the following propositions: p: I have a bike. q : It is sunny r: I will go biking. s will stay home Express the following propositions as English sentences: a) pA r