If anything is stuck in traffic, Bruno will be mad if it is late. Something is neither annoyed nor not late. If Bruno is mad, then something is annoyed. So something is not stuck in traffic.
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?
A) Mb ⊃ Ab
B) Mb ⊃ Ae
C) (∀x) ∼(Ax • ∼∼Lx)
D) (∃x)(Ax $ \lor $ ∼Lx)
E) ∼ (∃x)(∼Ax • ∼∼Lx)

Question

Quizplus · Accepted Answer

The first premise can be translated as "If Bruno is mad, then the thing is annoyed." Using contraposition, we can rewrite this as "If the thing is not annoyed, then Bruno is not mad." 
The second premise states that "Something is neither annoyed nor not late", which can be rewritten as "Something is not annoyed and not not-late", or simply "Something is not annoyed and is not late."
Combining these two statements gives us "Something is not annoyed and Bruno is not mad", which can be expressed using logic symbols as ∼(A • ∼Mb). Using De Morgan's laws, this can be rewritten as (∀x) ∼(Ax • ∼∼Lx). Therefore, C is an immediate consequence of the given premises.

If Anything Is Stuck in Traffic, Bruno Will Be Mad ∨ \lor ∨

If Anything Is Stuck in Traffic, Bruno Will Be Mad $\lor$