212 CHAPTER 3 Relations
Students
SocSecNo Name Major Class Year
247617832 Smith, John Mathematics^2005
477677251 Brown, Mae English 2006
149867253 Cyr, Pete Mathematics 2005
316719842 Williams, Sue English 2004Grades
SocSecNo CourseCode Grade
316719842 Math2l1 A
247617832 Engll03 B
149867253 Math214 A
149867253 Engll03 A
316719842 Math3l8 B
316719842 Eng1224 ACatalog
CourseCode Department Credits
Math2l1 Mathematics 4
Engl 103 English 3
Math214 Mathematics 3
Math318 Mathematics 4
Eng1224 English^3- Find the join of Grades and Catalog.
- Find the join of Students and Grades.
- Find the join of Students, Grades, and Catalog.
- Find all students who received an A in a course.
- Find the department and number of credits for any course in which a student received
an A. - Find all second-year students who received an A.
- Find the departments in which a student received an A in one of that department's
courses.
U Chapter Review
The idea of a relation gives a format for studying mathematical and nonmathematical re-
lationships. Forming the composition of relations and defining the inverse of a relation
are fundamental operations on relations. The common properties of relations such as =,
<, and C are abstracted to define what it means for a relation to be reflexive, irreflexive,
symmetric, antisymmetric, and transitive. Finding the reflexive, symmetric, or transitive
closure of a relation identifies the smallest relation containing a given relation with a given