Question

I need to write in prolog these first order statements. How are they to be written? red(X) should return false, green(X) should return false, and green(X) or red(X) should return true

I have this code already:

% Assigning Facts

apple(a).
apple(b).
orange(c).
pear(d).
carrot(e).
onion(f).
pepper(g).
% Assigning Rules

red(X) :- apple(X).
green(X) :- apple(X).

fruit(X) :- apple(X).
fruit(X) :- orange(X).
fruit(X) :- pear(X).

vegetable(X) :- carrot(X).
vegetable(X) :- pepper(X).

tasty(X) :- fruit(X).
tasty(X) :- carrot(X).
tasty(X) :- not(onion(X)).

vegetable(X) :- not(tasty(X)).

Answer 1

What is the ‘exists’ method in Prolog that you already know of?

How about:

red(X).               % ∃x Red(x)
green(X).             % ∃x Green(x)
(red(X) ; green(X)).  % ∃x Red(x) v Green(x)

Prolog will enumerate bindings of X which satisfy each call, or fail trying. If you just wanted to test their existence and not collect bindings, you can ignore the variable and cut after the first binding, like so:

red(_), !.

You’ve also asked how to test if something is exclusively red or green, but not both. Try this:

((\+ red(X), green(X)) ; (red(X), \+ green(X)).  % ∃x Red(x) ⊻ Green(x)

Where ⊻ means exclusive-or (XOR).