(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,
the values of x and y are stored in the same memory location during execution of the program.
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A relation on a set is if for every element .
A relation on a set is if whenever
A relation on a set is if and implies
A relation is an if the relation is transitive, symmetric and reflexive.
The of is the set of all elements that are relation to . Notation: