Exercises
[055] Prerequisites: [038], [04Z].(Solved on 2023-01-24) Let \(X\) be an infinite set, let \(∼\) be an equivalence relation on \(X\), let \(U=X/∼\) be the equivalence classes.
Suppose each class is finite, show that \(|U|=|X|\).
Suppose \(U\) is infinite and every class has cardinality at most \(|U|\), then \(|U|=|X|\).
Solution 1