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)).

this  is a computer science question please answer accordingly give neat and detailed explaination.