a)Consider the following formula, ∀x∀y(∃z(p(x, z) ∧p(z, y)) →g(x, y)) Use equivalences to construct a prenex normal form for the above wff. Show your work. Write down the number and name of the equivalence used at each step. b)Use equivalences to construct a prenex disjunctive normal form for the following wff. Show your work. Write down the number and name of the equivalence used at each step. ∀x∃yp(x, y) →∃y∀xp(x, y) c)Use equivalences to construct a prenex conjunctive normal form for the following wff. Show your work. Write down the number and name of the equivalence used at each step. ∀x∀y∀z(p(x, y) ∧p(y, z) →p(x, z)) ∧∀x¬p(x, x) →∀x∀y(p(x, y) →¬p(y, x)).
a)Consider the following formula,
∀x∀y(∃z(p(x, z) ∧p(z, y)) →g(x, y))
Use equivalences to construct a prenex normal form for the above wff. Show your work. Write down the
number and name of the equivalence used at each step.
b)Use equivalences to construct a prenex disjunctive normal form for the following wff. Show your work. Write down
the number and name of the equivalence used at each step.
∀x∃yp(x, y) →∃y∀xp(x, y)
c)Use equivalences to construct a prenex conjunctive normal form for the following wff. Show your work. Write down
the number and name of the equivalence used at each step.
∀x∀y∀z(p(x, y) ∧p(y, z) →p(x, z)) ∧∀x¬p(x, x) →∀x∀y(p(x, y) →¬p(y, x)).
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