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

question 129

Multiple Choice

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.
-Which of the following is the best translation into PL of this argument?

• A) H ≡ (P \( \lor \) Q) ∼(H ⊃ Q) / ∼(N • ∼P)
• B) H ≡ (P \( \lor \) Q) ∼(Q ⊃ H) / ∼N • ∼P
• C) H ≡ (P \( \lor \) Q) H ⊃ ∼Q / ∼(N • ∼P)
• D) H ≡ (P \( \lor \) Q) ∼(Q ⊃ H) / ∼(N • ∼P)
• E) H ≡ (P \( \lor \) Q) ∼(H ⊃ Q) / ∼N • ∼P

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Definitions:

Base Case

In recursion, the condition under which a recursive function returns without calling itself, effectively stopping the recursion.

Original Method

The initial or primary implementation of a method before it is overridden or modified by additional functionality.

General Case

A situation or condition that applies broadly, without special considerations or exceptions.

Recursive Algorithm

A method of solving a problem where the solution involves solving smaller instances of the same problem.