Question 11

1. Let the domain be mobile phones. Define predicates:

   • $G(x)$: $x$ is a good mobile phone.
   • $C(x)$: $x$ is a cheap mobile phone.

2. Formalize statement $P$:
   "Good mobile phones are not cheap":

   $$P: \forall x, (G(x) \to \neg C(x)).$$

3. Formalize statement $Q$:
   "Cheap mobile phones are not good":

   $$Q: \forall x, (C(x) \to \neg G(x)).$$

4. Recall that the contrapositive of an implication $A \to B$ is $\neg B \to \neg A$, and any implication is logically equivalent to its contrapositive.
   The contrapositive of $G(x) \to \neg C(x)$ is:

   $$\neg (\neg C(x)) \to \neg G(x) \iff C(x) \to \neg G(x).$$

   Hence, statement $P$ is logically equivalent to statement $Q$ ($P \equiv Q$).

5. Since $P \equiv Q$:

   • $P \implies Q$ is TRUE (statement $L$).
   • $Q \implies P$ is TRUE (statement $M$).
   • $P \iff Q$ is TRUE (statement $N$).

Therefore, $L$, $M$, and $N$ are all TRUE (option D).