Translate the following into English where Px is x is pink F

Translate the following into English, where P(x) is \"x is pink\", F(x) is \"x is fluffy\" and D(x) is \"x dances on rainbows\". The universe of discourse is all unicorns. - x(P(x) (F(x) -D(x))) x((D(x)_f(x)) rightarrow -P(x))

Solution

Here we denote

P(x) : x is pink

F(x) : x is fluffy

D(x) : x dances on rainbows

(a) Now consider the given quantified statement \" ¬ x ( P(x) ( F(x) ¬ D(x) ) )

We can write ¬ x ( P(x) ( F(x) ¬ D(x) ) ) x ¬ ( P(x) ( F(x) ¬ D(x) ) )

                                                                    x ( ¬ P(x) ¬ ( F(x) ¬ D(x) ) )

                                                                    x ( ¬ P(x) ( ¬ F(x) ¬ (¬ D(x) ) ) )

                                                                      x ( ¬ P(x) ( ¬ F(x) D(x) ) )

Thus , we have

                ¬ x ( P(x) ( F(x) ¬ D(x) ) ) x ( ¬ P(x) ( ¬ F(x) D(x) ) )

and we can write the symbolic form in English as follows :

\" All unicorns are not pinck or not fluffy or dances on rainbows \"

(b) Now consider the given quantified statement \" x ( ( D(x) ¬F(x) ) ¬ P(x) )

Then we can write the symbolic form in English as follows :

\" All unicorns that dance on rainbows and not fluffy are not pink \"