Complete answers or none please, Thanks: Define an appropriate language and form

Question

Complete answers or none please, Thanks:

Define an appropriate language and formalize the following sentences using FOL formulas. Justify your answers.

(a) Some people like math.

(b) Everyone loves some person who loves them self.

(c) No happy boy despises all animals.

(d) Some people are tall and thin.

(e) There are no mushrooms that are poisonous and purple.

(f) There is a mushroom that is purple and poisonous.

(g) There is only one Einstein (do not use !).

(h) All numbers greater or equal than one are bigger than themselves divided by four.

(i) Every box contains at least one coin.

(j) Bob’s sister knows Ann’s brother.

Explanation / Answer

FOL expressions are given below:

(a) Some people like math.

x(People(x) Like(x, math))

(c) No happy boy despises all animals.

¬x(HappyBoy(x) y( animals(y) despises(x, y)))

(d) Some people are tall and thin.

x(People(x)Tall(x)Thin(x))

(e) There are no mushrooms that are poisonous and purple.

¬x(Mushrooms(x)Poisonous(x)Purple(x))

(f) There is a mushroom that is purple and poisonous.

x(Mushrooms(x)Poisonous(x)Purple(x))

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