Answer
a. ∀ people x, ∃ a person y such that x trusts y.
b. negation: ∃ a person x, such that ∀ people y, x does not trust y. In other words, there is someone who does not trust anyone.
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.
