Suppose that the domain of the propositional function p(x) consists of −5, −3, −1, 1, 3, and 5. express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions.

a) ∃xp (x)
b) ∀xp (x)
c) ∀x((x ≠ 1) → p (x))
d) ∃x((x ≥ 0) ∧ p (x))
e) ∃x(¬p (x)) ∧ ∀x((x < 0) → p (x))