Chapter 1.4, Problem 50E

Exercises 48−51 establish rules fornull quantificationthat we can use when a quantified variable does not appear in part of a statement.

50. Establish these logical equivalences, wherexdoes not occur as a free variable inA. Assume that the domain is nonempty.

a) SS $\forall x\left(A\to P\left(x\right)\right)\equiv A\to \forall xP\left(x\right)$

b) $\exists x\left(A\to P\left(x\right)\right)\equiv A\to \exists xP\left(x\right)$