In 19–31, (1) prove that the relation is an equivalence

Chapter 8, Problem 24E

(choose chapter or problem)

Problem 24E

In 19–31, (1) prove that the relation is an equivalence relation, and (2) describe the distinct equivalence classes of each relation.

Let A be the set of identifiers in a computer program. It is common for identifiers to be used for only a short part of the execution time of a program and not to be used again to execute other parts of the program. In such cases, arranging for identifiers to share memory locations makes efficient use of a computer’s memory capacity. Define a relation R on A as follows: For all identifiers x and y,

x R y ⇔ the values of x and y are stored in the same memory location during execution of the program.