(∀X)[Px ⊃ (∃Y)Rxy] ⊃ [(∀X)(∀y)∼Rxy ⊃ ∼(∃X)Px]

question 173

Multiple Choice

(∀x) [Px ⊃ (∃y) Rxy] ⊃ [(∀x) (∀y) ∼Rxy ⊃ ∼(∃x) Px]
-Which of the following propositions is also derivable in F?

• A) (∀x)[Px ⊃ (∃y)Rxy] ⊃ [(∃x)~Px ⊃ (∃x)(∃y)Rxy]
• B) (∀x)[(∃y)Rxy ⊃ ~Px] ⊃ [(∃x)Px ⊃ (∃x)(∃y)Rxy]
• C) (∀x)[Px ⊃ (∃y)Rxy] ⊃ [(∃x)Px ⊃ (∃x)(∃y)Rxy]
• D) (∀x)[~(∃y)Rxy ⊃ Px] ⊃ [(∃x)Px ⊃ (∃x)(∃y)Rxy]
• E) (∀x)[Px ⊃ (∃y)Rxy] ⊃ [(∃x)~Px ⊃ (∃x)(∃y)~Rxy]

---

Definitions:

Copyright

A type of intellectual property protection that grants the creator exclusive rights to use, reproduce, and distribute their original works.

Equitable Estoppel

The principle that when a gratuitous promise to do something in the future causes a person who relies on that promise to incur an expense, the promisor will not be allowed to enforce other contractual rights that are inconsistent with that promise; the promise can only be used as a defense by the promisee; also known as promissory estoppel.

Natural Person

An individual human being, as opposed to a legal entity like a corporation or government.

Legal Bound

Being officially restrained by law or legally obliged to perform or refrain from performing certain actions.