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

The provided logical expressions describe various situations of student enrollment in classes, ranging from a specific student being in a particular class, to more complex scenarios involving multiple students and classes.

Step-by-step explanation:

The question involves interpreting expressions using predicate logic specifically within the context of a school's classes and students. Let's break down each expression:

• a) C(Randy Goldberg, CS 252): Randy Goldberg is enrolled in the CS 252 class.
• b) ∃xC(x, Math 695): There exists a student who is enrolled in Math 695.
• c) ∃yC(Carol Sitea, y): Carol Sitea is enrolled in some class.
• d) ∃x(C(x, Math 222) ∧ C(x, CS 252)): There exists a student who is enrolled in both Math 222 and CS 252.
• e) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) → C(y, z))): There exist two different students such that if one student is enrolled in a class, the other student is also enrolled in that class.
• f) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) ↔ C(y, z))): There exist two different students who are enrolled in exactly the same set of classes.

Answer 2

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.