Question

A discrete mathematics class contains 1 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 1 computer science major who is a senior. Express each of these statements 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 major.
c) There is a student in the class who is neither a mathematics 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

Answer 1

Answer and Step-by-step explanation:

As quantifiers, we can settle:

x is a student

M(x) is a math major student

C(x) is a computer science major student

F(x) is a freshman student

S(x) is a sophomore student

J(x) is a junior student

N(x) is a senior student

∃ exists

∀ every

¬ negation

∧ and

∨ or

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

∃xJ(x) value: True. There are 4 juniors

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

∀xC(x) value: False. There are math students

c) There is a student in the class who is neither a mathematics major nor a junior.

∃x¬M(x)∨¬C(x) value: False. All students are math ou computer science majors

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

∀xS(x)∨C(x) value: False. There are some students who are neither, for example mathematics majors who are juniors

e) There is a major such that there is a student*

∃M(x)C(x)x value: True. All majors have students.

*This one seems incomplete, but I answered the way it is writen.