Let C(x, y) mean that student x is enrolled in class y,

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) \(\exists x C(x\), Math 695)

c) \(\existsyC(\)Carol Sitea, y)

d) \(\exists x(C(x\), Math 222 \() \wedge C(x, \operatorname{CS} 252))\)

e) \(\exists x \exists y \forall z((x \neq y) \wedge(C(x, z) \rightarrow C(y, z)))\)

f) \(\exists x \exists y \forall z((x \neq y) \wedge(C(x, z) \leftrightarrow C(y, z)))\)

Equation Transcription:

∃xC(x

∃yC

∃x∃y∀z((x  y) ∧ (C(x, z) → C(y, z)))

∃x∃y∀z((x  y) ∧ (C(x, z) ↔ C(y, z)))

Text Transcription:

C(x, y)

\exists x C(x

\exists x(C(x

\exists x \exists y \forall z((x \neq y) \wedge(C(x, z) \rightarrow C(y, z)))

\exists x \exists y \forall z((x \neq y) \wedge(C(x, z) \leftrightarrow C(y, z)))