1. (20pts) Use the rules of inference and the laws of propositional logic to complete the proof of the following argument. s+t ot Complete the proof by filling in the empty space in each step: te Proposition Justification Conditional identities, 1 s +t 5 6 7. Hypothesis De Morgan's Law, 7 10 2. (10pts) Let M(z, y) be the statement "person a has seen movie y," where the domain for z is the set of all people and the domain for y is the set of all movies ever released Match each English statement with its equivalent logical expression in this list by putting the number of each logical expression in front of the corresponding English statement. English Statements Logical expressions Everyone has seen at least one movie. Some movies have been seen by everyone. Nobody has seen every movie. Every movie has been seen by at least one person 3) Vr3y M(x,y) Someone has seen every movie. 5) Vyar(a,y)