Question

Let C(x, y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being given at your school. Express each of these statements by a simple English sentence. a) C(Randy Goldberg, CS 252) b) ∃xC(x, Math 695) c) ∃yC(Carol Sitea, y) d) ∃x(C(x, Math 222) ∧ C(x, CS 252)) e) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) → C(y, z))) f) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) ↔ C(y, z)))

Answer 1

Answer:

a) C(Randy Goldberg, CS 252)

Randy Goldberg is enroled to class CS 252

b) ∃xC(x, Math 695)

There is a student that's enrolled to math clase 695

c) ∃yC(Carol Sitea, y)

There is a class where Carol Sitea is enrolled.

d) ∃x(C(x, Math 222) ∧ C(x, CS 252))

There is a student that's enrolled in math 222 class and in CS 252

e) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) → C(y, z)))

There are two students (that arn't the same person) that, for every class, if one is enrroled, the other is enrrolled too.

f) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) ↔ C(y, z)))

There are two students (that arn't the same person) that, for every class, they only are enrolled to the class if the other is enrroled too.

Answer 2

The statements are illustrations of variable quantification

From the question, we have:

1. C(x, y) represents student x enrolled in class y
2. y represents class
3. x represents students

Using the above representations, we have the following interpretations

(a) C(Randy Goldberg, CS 252)

Randy Goldberg is enrolled to class CS 252

b) ∃xC(x, Math 695)

x in the above statement means student.

So, the interpretation is:

There is a student that's enrolled to math 695 class

c) ∃yC(Carol Sitea, y)

y in the above statement means class.

So, the interpretation is:

There is a class where Carol Sitea is enrolled.

d) ∃x(C(x, Math 222) ∧ C(x, CS 252))

The symbol ∧ represents and

So, the interpretation is:

There is a student that's enrolled in math 222 class and in CS 252 class

e) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) → C(y, z)))

The symbol ≠ represents not equal to

So, the interpretation is:

There are two different students that, for every class, if one is enrolled, the other is enrolled too.

f) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) ↔ C(y, z)))

The interpretation is:

There are two different students that, for every class, they only are enrolled in the class if the other is enrolled too.

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