Owen will be happier if, and only if, he either practices the cello or quits music lessons. It is not that case that Owen quits music lessons only if he'll be happier. So, it is not the case that he both never sleeps and doesn't practice.
-Consider assuming 'N • ∼P' for an indirect proof of the given argument. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for indirect proof?
A) N
B) ∼P • N
C) ∼(∼Q $ \lor $ H)
D) (P $ \lor $ Q) ≡ H
E) All of the above

Question

Quizplus · Accepted Answer

The Answer of Owen will be happier if, and only if, he either practices the cello or quits music lessons. It is not that case that Owen quits music lessons only if he'll be happier. So, it is not the case that he both never sleeps and doesn't practice.
-Consider assuming 'N • ∼P' for an indirect proof of the given argument. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for indirect proof?
A) N
B) ∼P • N
C) ∼(∼Q $ \lor $ H)
D) (P $ \lor $ Q) ≡ H
E) All of the above

Owen Will Be Happier If, and Only If, He Either ∨ \lor ∨

Owen Will Be Happier If, and Only If, He Either $\lor$