1. ∼A ≡ B
2. A • ∼C
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
A) ∼(A ≡ B)
B) B ≡ ∼A
C) ∼∼A ≡ ∼B
D) Options A, B, and C
E) Options A and B, but not option C

Question

Quizplus · Accepted Answer

The given premises are:1. ∼A ≡ B2. A • ∼CFrom premise 1, we can derive:∼(A ≡ B) ≡ ∼BFrom premise 2, we can derive:A ≡ ∼∼CSubstituting the derived equivalence from premise 2 into the derived equivalence from premise 1, we get:∼(A ≡ B) ≡ ∼∼CSimplifying this equivalence, we get:∼∼A ≡ ∼BTherefore, options A, B, and C are all immediate consequences of the given premises.