Consider the following infinite set of propositional formulas, based on the atomic propo- sitions po, P1, P2, ... U = {po PP1 P2 P2P psp ...} (a) 4 points Is U satisfiable? Explain your answer. (b) 2 points for what values of n does U have the following logical consequences: UP = P2? UPP? (c) 2 points for what values of n are the following sets satisfiable? UU{po Pan}: UU{po P2} . Consider the following infinite set of propositional formulas, based on the atomic propo- sitions po, P1, P2, ... U = {po PP1 P2 P2P psp ...} (a) 4 points Is U satisfiable? Explain your answer. (b) 2 points for what values of n does U have the following logical consequences: UP = P2? UPP? (c) 2 points for what values of n are the following sets satisfiable? UU{po Pan}: UU{po P2}