Answers

1. Translate these wffs in PL into English. "Bz" means x is a bird and "Fz" means z can fly.

• ∀zBz - Everything is a bird.
• ~∀z~Bz - It is not the case that everything is not a bird. (That is, something is a bird, or there is at least one bird.)
• ~∃zFz - It is not the case that there is something that can fly. Or, nothing can fly.
• ∃z~Fy - There is something that cannot fly.
• ∀z~~Bz - Everything is a bird.

2. Use the quantifier exchange rules to rewrite each of above wffs into a different but logically equivalent wff.

• ∀zBz becomes ~∃z~Bz using QE1.
• ~∀z~Bz becomes ~~∃z~~Bz using QE1.
• ~∃zFz becomes ~~∀z~Fz using QE2.
• ∃z~Fy becomes ~∀z~~Fz using QE2.
• ∀z~~Bz becomes ~∃z~~~Bz using QE1

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