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How to do 2 equal formulas using only one type of quantifier

(∃a)(∀b)(∃c)(∀d)(a · c = d · b)

I have to use only ∀ in the first formula and only ∃ in the second formula.

lasto
  • 81
  • Think about the deMorgan laws. –  Oct 19 '19 at 10:11
  • @MatthewDaly 1) ¬(∀a)¬(∀b)(∀c)(∀d)(a . c = d . b) and 2) (∃a)¬(∃b)¬(∃c)(∃d)(a . c = d . b) ? – lasto Oct 19 '19 at 16:30
  • You'd have to wrap negations around both quantifiers you're shifting. But, yeah, I don't think it's anything more complicated than that. –  Oct 19 '19 at 18:25
  • ¬(∀a)(∀b)¬(∀c)(∀d)(a . c = d . b) and 2) (∃a)¬(∃b)(∃c)¬(∃d)(a . c = d . b)
    • – lasto Oct 20 '19 at 16:26