Answer
a. False. There is no triangle above circle b.
b. Formal version: ∃x(Triangle(x) ∧ (∀y(Circle(y) → Above(x, y))))
c. Formal negation: ∀x(∼Triangle(x) ∨ (∃y (Circle (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.
Formal logical notation:
"$\forall x$ in D, P(x)" can be written as $\forall x$ (x in D $\rightarrow$ P(x)).
"$\exists x$ in D such that P(x)" can be written as "$\exists x$ (x in D $\land$ P(x))."
