Respuesta :
Answer:
a. ∃s ∈D such that M(s) ∧ E(s)
b. Vs ∈D, C(s) → E(s)
c. Vs ∈D, C(s) → ~ E(s)
d. ∃s ∈D such that M(s) ∧ C(s)
e. (∃s ∈D such that C(s) ∧ E(s)) ∧ (∃t ∈D such that C(t) ∧ ~ E(t))
Step-by-step explanation:
Given
D = set of all students in your school ---- Doman
M(s) = "is a Math major"
C(s) = "is a computer science student"
E(s) = "is an engineering student"
a. There is an engineering student who is a math major.
We can rewrite the above expression as:
"There's at least one student s ∈ D such that s is a math major and s is an engineering student".
The statement "There's at least one" implies an existential statement.
An existential statement is defined as ∃x:P(x) and it is true if amd only if there is an existence of at least one element in the domain.
So, we'll replace
"s is a math major" with M(s)
"s is an engineering student" with E(s)
"and" with ∧.
Bringing them together, we have
∃s ∈D such that M(s) ∧ E(s)
b. Every computer science student is an engineering student.
We can rewrite the above expression as:
"For every student s ∈ D if s is a computer science student then s is an engineering student".
The statement "For every" implies an universal statement.
A universal statement is defined as VxP(x) and is true if and only if P(x) is true for all values of X in the domain.
So, we'll replace
"s is a computer science student" with C(s)
"s is an engineering student" with E(s)
"If then" with →
Bringing them together, we have
Vs ∈D, C(s) →E(s)
c. No computer science students are engineering students.
We can rewrite the above expression as:
"For every student s ∈ D if s is a computer science student then s is not an engineering student".
The statement "For every" implies an universal statement.
A universal statement is defined as VxP(x) and is true if and only if P(x) is true for all values of X in the domain.
So, we'll replace
"s is a computer science student" with C(s)
"s is an engineering student" with E(s)
"If then" with →
"not" by ~
Bringing them together, we have
Vs ∈D, C(s) → ~ E(s)
d. Some computer science students are also math majors.
We can rewrite the above expression as:
"There's at least one student s ∈ D such that s is a math major and s is an computer science student".
The statement "There's at least one" implies an existential statement.
An existential statement is defined as ∃x:P(x) and it is true if and only if there is an existence of at least one element in the domain.
So, we'll replace
"s is a math major" with M(s)
"s is a computer science student" with C(s)
"and" with ∧.
Bringing them together, we have
∃s ∈D such that M(s) ∧ C(s)
e. Some computer science students are engineering students and some are not.
We can rewrite the above expression as:
"There's at least one student s ∈ D such that s is a computer science student and s is an engineering student" and "There's at least one student t ∈ D such that t is a computer science student and t is not an engineering student"
The statement "There's at least one" implies an existential statement.
An existential statement is defined as ∃x:P(x) and it is true if and only if there is an existence of at least one element in the domain.
So, we'll replace
"s is a computer science student" with C(s)
"s is an engineering student" with E(s)
"and" with ∧.
"not" with ~
Bringing them together, we have
(∃s ∈D such that C(s) ∧ E(s)) ∧ (∃t ∈D such that C(t) ∧ ~ E(t))
