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**TTim** I am doing my first maths class since high school three years ago and I'm having trouble at getting my head around the abstraction of equivalence relations.

The following table gives a list of 6 different relations.

a) Which of the relations are equivalence relations? Mark anXin the column under “is equivalence relation?”for those which are equivalence relations.

b) For those which are equivalence relations, give an example of an equivalence class (i.e., choose an elementxof the set, and write a list of all the elements equivalent tox, or a formula for all the elements if this isan inﬁnite set).

c) For those which are equivalence relations, in the last column of the table, write down the number ofequivalence classes (this could be inﬁnite.)

Each relation in this table is a relation on a given set, listed under “set”.

Set / Relation

1. R /aRb ⇐⇒ a−b is negative