The dentist is pleased if, and only if, I both brush and floss. The dentist is not pleased, but I brush. So, I don't floss.
-Which of the following is the best translation into PL of this argument?
A) P ⊃ (B • F) ∼P • F / ∼F
B) P ≡ (B • F) ∼P • B / ∼F
C) P ≡ (B • F) ∼P $ \lor $ B / ∼F
D) (P ≡ B) • F ∼P $ \lor $ B / ∼F
E) (P ≡ B) • F ∼P • B / ∼F

Question

Quizplus · Accepted Answer

The correct translation reflects the logical structure of the argument: "The dentist is pleased if and only if I both brush and floss" translates to $P \equiv (B \cdot F)$, indicating that the dentist being pleased is equivalent to both brushing and flossing happening. "The dentist is not pleased, but I brush" translates to $\sim P \cdot B$, indicating the dentist is not pleased and I brush. The conclusion "So, I don't floss" translates to $\sim F$. This structure is accurately represented in choice B.

The Dentist Is Pleased If, and Only If, I Both ∨ \lor ∨

The Dentist Is Pleased If, and Only If, I Both $\lor$