Symbolization with Identity — 9.1ex II

Symbolize the following.

universe of discourse: all people
b: Bill Clinton
g: George W. Bush
u: the United States
s: the Supreme Court		 Cx: x is a country
Fx: x is female
Pxy: x is president of y
Ixy: x = y
Lxy: x leads y
  1. George is US president and Bill is not. (Hint)
  2. George is the (one and only) president of the Supreme Court. (Hint)
  3. There is more than one president of the US. (Hint)
  4. There is exactly one president of the US. (Hint)
  5. There is no president of the US.
  6. There are at least two countries.(Hint)
  7. There is at most one country. (Hint)
  8. At least one female leads a country. (Hint)
  9. At most one person leads the US. (Hint)
  10. No one but George leads the US. (Hint)