Hello, I would like to ask if my predicate logic translation is correct for the

Question

Hello, I would like to ask if my predicate logic translation is correct for the below question since I still have a bit of trouble visualizing the equations. If it's wrong, can you please correct me? Thank you!

Consider the following predicates over the domains A of all animals, CM of all BC
cabinet ministers, and MS of all movie stars.
• L(x, y): person x likes person y.
• S(x, y): x is scared of animal y.

Rewrite each of the following statements using only the quantifiers and , the predicates L and S, the domains A, CM and MS, logical connectives, and the operators = and .

a) No movie star likes a cabinet minister who does not like that movie star.
y CM, ~(x MS, L(x,y) ^ ~(L(y,x)))
b) Movie stars like cabinet ministers who are not scared of any animal.
xMS, yCM, zA, ~(S(y,x)) -> L(x,y)
c) There is a cabinet minister who can talk to every movie star about an animal
of which they are both scared.
xCM, yMS, zA, L(x,y) ^ (S(x,z) ^ (S(y,x))
d) There are two BC cabinet ministers who are scared of the same animals but
do not have exactly the same taste in movie stars.
x,yCM, p, qA, (S(x,p) ^ S(y,p), p=q) ^ (~r, sMS, (L(x,r) ^ L(y,s), r=s))

Explanation / Answer

Solutions:

The below logic translations are perfectly correct.

a) y CM, ~(x MS, L(x,y) ^ ~(L(y,x)))

b)xMS, yCM, zA, ~(S(y,x)) -> L(x,y)

c) xCM, yMS, zA, L(x,y) ^ (S(x,z) ^ (S(y,x))

d) x,yCM, p, qA, (S(x,p) ^ S(y,p), p=q) ^ (~r, sMS, (L(x,r) ^ L(y,s), r=s))

D point can also be written as below (variables changed)

c1 CM, c2 CM, a A, s Ms, c1 c2   S(c1,a) S(c2,a) ( (L(c1,s)~L(c2,s)) v (~L(c1,s)L(c2,s)))

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