Question

Can somebody explain to me how to get the answer of this proposition?

Express the negations of these propositions using quantifiers, and in English.

"There is a student in this class who has been in at least one room of every building on campus."

Answer 1

Solution:

Given condition is "There is a student in this class who has been in at least one room of every building on campus."

Here Objective is Express the negations of these propositions using quantifiers, and in English.

Consider that x: student in the class

y: Building on campus

z: rooms

Here the condtions are

M(z,y): Room z in building y

N(x,y) : Student x visited in room z

Negotiation of the above proposition is represented as below,

­­­­¬Ǝx˄­­­­­­­­­­­­Ǝy­ ˄­­­­­­­­­­­­[∀z M(z,y) => N(x,z)]

In Engish we can tell as "There are no students who have visited every room of at least one building on campus"

Hence as per the above sentence , the given statement can be written as

¬Ǝx˄­­­­­­­­­­­­Ǝy­ ˄­­­­­­­­­­­­[∀z M(z,y) => N(x,z)].

Finally we can express the negation as "There are no students who have visited every room of at least one building on campus"