Consider the first-order logic sentence F:∀x(∃yR(x,y)). Assuming non-empty logical domains, which of the sentences below are impied by F ?I ∃y(∃xR(x,y))II ∃y(∀xR(x,y))III ∀y(∃xR(x,y))IV ⇁∃x(∀y⇁R(x,y))

Consider the first-order logic sentence F:∀x(∃yR(x,y)). Assuming n

1.	Consider the first-order logic sentence F:∀x(∃yR(x,y)). Assuming non-empty logical domains, which of the sentences below are impied by F ?I ∃y(∃xR(x,y))II ∃y(∀xR(x,y))III ∀y(∃xR(x,y))IV ⇁∃x(∀y⇁R(x,y))
Answer» Consider the first-order logic sentence $F : \forall x (\exists y R (x, y))$ . Assuming non-empty logical domains, which of the sentences below are impied by F ? I $\exists y (\exists x R (x, y))$ II $\exists y (\forall x R (x, y))$ III $\forall y (\exists x R (x, y))$ IV $⇁ \exists x (\forall y ⇁ R (x, y))$