Question

A discrete mathematics class contains I mathematics

major who is a freshman, 12 mathematics majors who

are sophomores, 15 computer science majors who are

sophomores. 2 mathematics majors who are juniors. 2

computer science majors who are juniors, and I computer

science major who is a senior. Express each of these state-

ments in terms of quantifiers and then determine its truth

value.

a) There is a student in the class who is a junior.

b) Every student in the class is a computer science ma-

jor.

c) There is a student in the class who is neither a math-

ematics major nor a junior.

d) Every student in the class is either a sophomore or a

computer science major.

e) There is a major such that there is a student in the

class in every year of study with that major.

Choosing the correct answer step by step

Answer 1

student(x) - x is a student in the class, junior(x) - x is a junior, computer(x) - x is a computer science major, math(x) - x is a math major, sophomore(x) - x is a sophomore, major(x) - x is a major, class(x) - x is the year of the class, atudy(x, y) - x studies y

a) There is a student in the class who is a junior

$\exist x:(student(x)\land junior(x))$ - true

b) Every student in the class is a computer science major.

$\forall x:(student (x)\to computer(x))$ - false

c) There is a student in the class who is neither a math-

ematics major nor a junior.

$\exist x:(student(x) \land \lnot(math(x)\lor junior(x)))$ - true

d) Every student in the class is either a sophomore or a computer science major.

$\forall x:(student(x)\to (sophomore(x)\lor computer(x)))$ - false

e) There is a major such that there is a student in the

class in every year of study with that major.

$\exist x\forall y\exists z:(major(x) \land student(z) \land class(y) \land study(z,x))$ - false