Give a quantified expression that is logically equivalent to each of the following statements.

I. (10 points) A student club holds an election for officers. Before the voting., members can nominate cach other. It is also possible for a member to nominate himself or herself. Some of the members are new members. Some of the members are currently officers. The domain is the set of members of the club. One of the members of the club is named Sam. Define the following predicates N(z, y): person W(): person z is a new member. nominated person y for a position. 0(x): person x is currently an officer. Give a quantified expression that is logically equivalent to each of the folloiwng statements (a) All the new members nominated all the officers. (b) One of the current officers did not nominate anyone. (c) Everyone nominated someone