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 propositions is an immediate (one-step) consequence in PL of the given premises?
A) ∼P ≡ (B • F)
B) ∼P ≡ ∼(B • F)
C) ∼[P ≡ (B • F)]
D) ∼(B • F) ≡ P
E) None of the above

Question

Quizplus · Accepted Answer

Let P be "The dentist is pleased"
Let B be "I brush"
Let F be "I floss"
From the premises, we know that P is false (the dentist is not pleased) and B is true (I brush). Therefore, using the fact that the dentist is pleased if and only if I both brush and floss, we can conclude that F is false (I don't floss).
The equivalent form of "I don't floss" in PL is ∼(B • F). Therefore, the immediate consequence in PL of the given premises is ∼P ≡ ∼(B • F), which is choice B.

The Dentist Is Pleased If, and Only If, I Both