Question

Question 2: Formalization of Logical Expressions

Translate the following statements into predicate calculus. If you name your predicates intuitively, you do not have to define them separately.

a) Jenna watches only funny movies.

b) Ernie knows all of Bert’s friends.

c) Petra and Paula do not take any classes together.

e) Carl beats up all professors that fail him.

f) There is at most one computer scientist who can dance.

g) There are no scientists who are neither crazy nor dangerous.

Answer 1

a)

b) $\forall x (friendOfBert(x) \Rightarrow ErnieKnows(x))$

c) $\neg (\exists x (PetraTakes(x)\wedge PaulaTakes(x)))$

e) $\forall x (Fails(x) \Rightarrow CarlBeats(x))$

f)

A = There is no computer scientist who can dance => $\neg \exists x (ComputerScientist(x) \Rightarrow Dance(x))$

B = There is one computer scientist who can dance =>

$\exists x (ComputerScientist(x) \wedge Dance(x) (\forall y)(ComputerScientist(y) \wedge Dance(y)\Rightarrow x = y))$ There exists at most one = A V B

$(\neg \exists x (ComputerScientist(x) \Rightarrow Dance(x)))) \vee (\exists x (ComputerScientist(x) \wedge Dance(x) (\forall y)(ComputerScientist(y) \wedge Dance(y)\Rightarrow x = y)))$

g) $\neg(\exists x(\neg Crazy(x) \wedge \neg Dangerous(x)))$