1. Write the inverse of the following conditional statement as an English sentence in the form "if p, then q." "To pass the exam, it is sufficient to study for the exam." 2. Let S(x,y) be the statement x has sent an email to y," where the domain of x and y consists of all people. Write the following sentence as a logical expression (i.e., using predicates, quantifiers, and logical operators). There is exactly one person who has been sent an email by everyone." 3. Write the following argument in argument form (i.e., using predicates and logical operators). "If I play hockey, then I am sore the next day. I go to the doctor when I am sore. Therefore, I go to the doctor whenever I play hockey." 4. Write the assumption (i.e., what you suppose) in a proof by contradiction of the following statement. "If a group of 3 kids ate a total of 13 candies, then at least one of the kids ate at least 5 candies