Answer
a. Formal version: ∃ a person x such that ∀ people y, x trusts y.
b. Negation: ∀ people x, ∃ a person y such that x does not trust y. In other words, everyone has someone whom they do not trust.
Work Step by Step
Recall the negation of a for all statement:
~($\forall x$ in D, P(x)) $\equiv \exists x$ in D such that ~P(x).
Recall the negation of an exists statement:
~($\exists x$ in D, P(x)) $\equiv \forall x$ in D such that ~P(x).
To negate a multiply quantified statement, apply the laws in stages moving left to right along the sentence.
