Chapter 1 - Section 1.5 - Nested Quantifiers - Exercises - Page 64: 6

a. Randy Goldberg is enrolled in class CS 252. b. There exists a student x that is enrolled in class Math 695. c. There exists a class y that Carol Sitea is enrolled in. d. There exists a student x that is enrolled in class Math 222 and is enrolled in class CS 252. e. There exists a student x and a student y such that for every class 2, student x and student y are not the same student and if x is enrolled in class 2 then y is also enrolled in class 2. f. There exists a student x and a student y such that for every class 2, student x and student y are not the same student and x is enrolled in class 2 if and only if y is enrolled in class 2.

a. Randy Goldberg is enrolled in class CS 252. C(x, y) means student, x is enrolled in class y b. There exists a student x that is enrolled in class Math 695. C(x, y) means student, x is enrolled in class y $\exists $ means there exists. c. There exists a class y that Carol Sitea is enrolled in. C(x, y) means student, x is enrolled in class y $\exists $ means there exists. d. There exists a student x that is enrolled in class Math 222 and is enrolled in class CS 252. C(x, y) means student, x is enrolled in class y $\exists $ means there exists and $\land$ means AND. e. There exists a student x and a student y such that for every class 2, student x and student y are not the same student and if x is enrolled in class 2 then y is also enrolled in class 2. C(x, y) means student, x is enrolled in class y $\exists $ means there exists, $\land$ means AND, $\rightarrow$ means IF-THEN, $\forall$ means FOR EVERY f. There exists a student x and a student y such that for every class 2, student x and student y are not the same student and x is enrolled in class 2 if and only if y is enrolled in class 2. $\exists $ means there exists, $\land$ means AND, $\leftrightarrow$ means IF-AND-ONLY-IF, $\forall$ means FOR EVERY