1. (5pts) Determine, for each statement, whether it is a proposition. Justify your answer in either case. (a) "Truth always wins." (b) "Be brave!" (c) "Fiction is a genre of literature and it is liked by all." (d) "Are you kind to yourself?" (e) "If five cats can catch five mice in five minutes, then one cat can catch one mouse in five minutes." 2. (6pts) Let x be the proposition "You get an A+on the final exam.", y be the proposition "You do every exercise in this book.". Translate the following expressions into English. (a) yx (b) yx (c) xy 3. (6pts) Let a be the proposition "It is below freezing", b be "It is snowing", and c be "I am cold". Translate the following expressions into English. (a) abc (b) c(ayb) (c) (ac)a. Simplify this statement before translating and show your work. 4. (10pts) Translate the following English expressions into logical statements. You must explicitly state what the atomic propositions are (e.g., "Let p be proposition ...") and then show their logical relation. (a) It is not true that blueberries are blue, but they are tasty. (b) If George were a spider, he would have eight legs. (c) When my day is tough, I find strength in a cup of coffee with croissant or chocolate. Hint: Look for three simple facts. (d) If it is not true that it is raining or windy, then it is cold if and only if it is snowing. (e) If I flip a coin it must come up either heads or tails. 5. 8pts) What is the negation of each of these proposition? Start by translating each English statement into logic. You must explicitly state what are the atomic propositions. Then, negate the obtained logical statement. After that translate the negated logical statement back into English. (a) 89 is a Fibonacci number. (b) If you drive more than 400 miles, you need to rest or buy gasoline. (c) Am and Om came to the meeting. (d) If you eat healthy and exercise regularly you will boost your immune system