1. Any professional can outplay any amateur. Jones is a professional but he cannot outplay Meyers. Therefore, Meyers is not an amateur. (Px: x is a professional; Ax: x is an amateur; Oxy: x can outplay y)

2. Whoever is a friend of either Michael or Paul will receive a gift. If Michael has any friends, then Eileen is one of them. Therefore, if Ann is a friend of Michael, then Eileen will receive a gift. (Fxy: x is a friend of y; Rx: x will receive a gift)

3. A horse is an animal. Therefore, whoever owns a horse owns an animal. (Hx: x is a horse; Ax: x is an animal; Oxy: x owns y)

4. O'Brien is a person. Furthermore, O'Brien is smarter than any person in the class. Since no person is smarter than himself, it follows that O'Brien is not in the class. (Px: x is a person; Sxy: x is smarter than y; Cx: x is in the class)

5. If there are any honest politicians, then if all the ballots are counted they will be reelected. Some honest politicians will not be reelected. Therefore, some ballots will not be counted. (Hx: x is honest; Px: x is a politician; Bx: x is a ballot; Cx: x is counted; Rx: x will be reelected)

Translate the following arguments into symbolic form. Then derive the conclusion of each, using conditional proof or indirect proof when needed.