Problem 6. (from Discrete Mathematics by Kenneth Rosen, based on questions found in the bo Logic by Lewis Carroll.) Let P(x), Q(x), R(x), and S(x) be the statements P(x): is a duck Q(x): is one of my poultry R(x: ax is an officer. S(x): ris willing to waltz The domain is the set of all poultry. Express each of the statements in 6(a) - 6(d) using quantif connectives; and P(x), Q(x), R(x), and S(a) 6(a) No ducks are willing to waltz. 6(b) No officers ever decline to waltz. 6(c) All my poultry are ducks. 6(d) My poultry are not officers 6(e) Is it possible that I have a poultry that is willing to waltz? Explain briefly