Express this statement using quantifiers Every student in th

Express this statement using quantifiers: \"Every student in this class has taken some course in every department in the school of mathematical sciences.\" Express this statement using quantifiers: \"There is a building on the campus of some college in the United States in which every room is painted white.\" Express the statement \"There is exactly one student in this class who has taken exactly one mathematics class at this school\" using the uniqueness quantifier. Then express this statement using quantifiers, without using the uniqueness quantifier.

Solution

a. every student in this class has taken some sources in every department in the school of mathematics science

variables: s student, c course & d department

domain: this class, all courses & department in the school of mathematical science

propositional function:P(s, c, d) =s took course c in department d.

entence can be written as: sdc P(s, c, d).

b) There is a building on the campus of some college on united states in the united states in which every room is painted white.

Let W(r) is that room r which is painted white.

Let B(r,b) is that room r is in building b.

Let L(b,u) is that building b is on the campus of United States university u.

Then, the statement is that there is some university u and some building b on the campus of u such

that every room in b is painted white.

In symbols, i.e., ub(L(b,u))r(B(r,b)-->W(r))).

c) xz((yw(T (z, w) w = y)) z = x)