The answers to exercises marked IBB] can be found in the Back of the Book.
[BB] Let A be the set of all natural numbers and ~ be as in Exercise. Show that ~ defines an equivalence relation on A.
The answers to exercises marked IBB] can be found in the Back of the Book.
[BB] Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. For a, b ∈ A, define a ~ b if and only if ab is a perfect square (that is, the square of an integer).
(a) What are the ordered pairs in this relation?
(b) For each a ∈ A, find ā = {x ∈ A | x ~ a).
(c) Explain why ~ defines an equivalence relation on A.
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