Answer
a. True. Both triangles a and c lie above all the squares.
b. Formal version: ∃x(Triangle(x) ∧ (∀y(Square(y) → Above(x, y))))
c. Formal negation: ∀x(∼Triangle(x) ∨ (∃y (Square (y)∧ ∼Above(x, y))))
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.
Negation of $\land$ is $\lor$. Negation of $\lor$ is $\land$.
