P: Eminem is the real Slim Shady.
Q: Eminem wins a Grammy.
R: Eminem is a rapper.
S: Christina Aguilera is the real Slim Shady.
T: Christina Aguilera wins a Grammy.
U: Christina Aguilera is a rapper.
V: Eminem is misogynistic.
W: Eminem is controversial.
1. Eminem, who is a rapper, is controversial if he is misogynistic.
R & (V -> W)
2. Unlike Eminem, Christina Aguilera is not the real Slim Shady.
P & ~S
3. Only one of Eminem and Christina Aguilera is the real Slim Shady.
(P v S) & ~(P & S)
4. Given that Eminem won’t win a Grammy if he is controversial and misogynistic, he won’t win a Grammy.
(W & V -> ~Q) -> ~Q
5. Eminem’s being misogynistic is sufficient but not necessary for him to be controversial.
(V -> W) & ~(W -> V)
6. If Eminem’s being controversial is either necessary or sufficient for him to be the real Slim Shady, then he is the real Slim Shady.
(P -> W) v (W -> P) -> P
7. Eminem is the real Slim Shady provided that Christina Aguilera is not.
~S -> P
8. If Eminem and Christina Aguilera are both rappers, then they will both win Grammys if either of them does.
R & U -> (Q v T -> Q & T)
9. Only on the condition that neither Eminem nor Christina Aguilera is a rapper will they both win Grammys, assuming that at least one of them is the real Slim Shady.
P v S -> (Q & T -> ~(R v U))
P v S -> (Q & T -> ~R & ~U)
10. Assuming that Christina Aguilera fails to be the real Slim Shady, she won’t win a Grammy unless she is a rapper.
~S -> (~U -> ~T)
~S -> (~T v U)
11. Unless Eminem, who is a rapper, is the real Slim Shady, it’s not the case that he is both controversial and misogynistic.
R & (~P -> ~(W & V))
R & (~P -> ~W v ~V)
R & (P v ~(W & V))
R & (P v (~W v ~V))
12. If Eminem is misogynistic if and only if he is a rapper, then his being controversial would imply that he will not win a Grammy.
(V <-> R) -> (W -> ~Q)