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By Esposito P.

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D) C4 - the set of fourth year students. 2. Let A be a set of 23 men standing on a football field. We can partition A into two classes of eleven elements each (the teams), and one class with one element (the referee). 3. We can partition the set of all human beings at a specified time into classes according to the day and month of birth. This gives us 366 different classes. If P is a partition of A, and if its classes are defined by certain properties, then each element of a specific class has the property which defines the class; in other words all the elements of a class are indistinguishable or equivalent with respect to the defining property of the class.

3. We can partition the set of all human beings at a specified time into classes according to the day and month of birth. This gives us 366 different classes. If P is a partition of A, and if its classes are defined by certain properties, then each element of a specific class has the property which defines the class; in other words all the elements of a class are indistinguishable or equivalent with respect to the defining property of the class. I. D ÜNTSCH & G. G EDIGA 33 Our next aim is to show that equivalence relations and partitions are just two sides of the same coin: Each equivalence relation induces a unique partition and vice versa.

ARb iff a ≤ b. Then R is a linear order on A. 3. 3) a/b iff a divides b. To show that / is a partial order we have to show the three defining properties of a partial order relation: Reflexive: Since every natural number is a divisor of itself, we have a/a for all a ∈ A. Antisymmetric: If a divides b then we have either a = b or a usual ordering of N; similarly, if b divides a, then b = a or b a b and b a is not possible, a/b and b/a implies a = b. b in the a. Since Transitive: If a divides b and b divides c then a also divides c.

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