#6 c and d. Express each of these quantifications in English. a) exist x P (x) b

Question

#6 c and d.

Express each of these quantifications in English. a) exist x P (x) b) Forall x P(x) c) exist x P(x) d) Forall x P(x) Let N(x) be the statement "x has visited North Dakota, " where the domain consists of the students in your school. Express each of these quantifications in English. a) exist x N(x) b) Forall x N(x) c) exist x N(x) d) exist x N(x) e) Forall x N(x) f) Forall x N(x) Translate these statements into English, where C(x) is "x is a comedian", and F(x) is "x is funny" and the domain consists of all people. a) Forall x(C(x) rightarrow F(x)) b) Forall x (C(x) Lambda F(x))

Explanation / Answer

Hi,

here given N(x) is given as "x has visited north dakota"
now, the inverted E stands for "there exists atleast one", so looking at the c) without negation we get

"There exists alteast one student in school who visited north dakota". lets convert it mathematically let n be the number of students who visited north dakota, so this becomes n>=1, now negation of this is n<1
which translates to "less than one of the students have been to north dakota" which is nothing but,
"There isnt anyone in the school who visited north dakota"
d) In this one, negation is on N(x) that means student didnt visit north dakota. now adding an atleast one to it we get "There exists atleast one student in the school who didnt visit North Dakota"
Thumbs up if this was helpful, otherwise let me know in comments. Good day.

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