1. Consider the following predicates over the domains A of all animals, CM of al

Question

1. 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.

b. Movie stars like cabinet ministers who are not scared of any animal.

c. There is a cabinet minister who can talk to every movie star about an animal of which they are both scared.

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.

2. Using the same definitions as for the first question, translate each of the following predicate logic statements into English. Try to make your English translations as natural sounding as possible.

a. c CM, s MS, L(c, s) L(s, c)

b. c1 CM, c2 CM, c1 c2 s MS, L(s, c1) L(s, c2) (c3 CM, c1 6= c3 c2 6= c3 L(s, c3))

c. c1 CM, s MS, c2 CM, c1 c2 L(c2, s) L(c1, s)

Explanation / Answer

1.a)s MS, c CM, ~L(c,s) ~L(s,c)

1.b)c CM, a A, s Ms, ~S(c,a) L(s,c)

1.c) for this let a predicate T(x,y,z) : x talks to y about z

c CM, s Ms, a A, S(c,a) S(s,a) T(c,s,a)

1.d)

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)))

2.a.) there is a movie star who doesn't like any cabinet minister but every cabinet ministers like him

2.b.)sorry I couldn't solve this part

2.c.)the simplified predicate logic expression will be

c1 CM, s MS, c2 CM, c1 c2 L(c2, s) L(c1, s)

so its translation will be: The movie stars who are not loved by people other than cabinet ministers are loved by cabinet ministers.

//If you have any doubt regarding the answer please ask in the comment box

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