Consider the following statements: $\text{P:}$ Good mobile phones are not cheap $\text{Q:}$ Cheap mobile phones are not good $\text{L: P}$ implies $\text{Q}$ $\text{M: Q}$ implies $\text{P}$ $\text{N: P}$ is equivalent to $\text{Q}$ Which one of the following about L, M, and N is $\textbf{CORRECT}$?

Let the universe of discourse be the set of all mobile phones. Define the predicates:

• $G(x)$: $x$ is a good mobile phone

• $C(x)$: $x$ is a cheap mobile phone

The statements can be formalized in first-order logic as:

• $$\text{P}$: \forall x\,(G(x) \implies

eg C(x))$

• $$\text{Q}$: \forall x\,(C(x) \implies

eg G(x))$

By the contrapositive law of propositional logic: $$G(x) \implies eg C(x) \equiv C(x) \implieseg G(x)$$

Thus, $\text{P}$ and $\text{Q}$ are logically equivalent:

• $\text{P} \implies \text{Q}$ is true (Statement L).

• $\text{Q} \implies \text{P}$ is true (Statement M).

• $\text{P} \iff \text{Q}$ is true (Statement N).

Therefore, L, M, and N are all TRUE, making (D) the correct option.