**2.1 Proof Involving Sets**

This is the first section of the second chapter in Mathematical Thinking and Writing book. It is time to begin applying the language and logic of chapter 1 to prove writing. A a good place to do this is with sets. In this section, we address two things. First, we return to the set terminology from chapter 0, and we use to practice some of the concepts we’ve learned so far. second, we get our feet wet by beginning to write proofs. Right of the bat, we’ll see three useful techniques for writing proofs: direct proofs, proofs by contrapositive and proofs by contradiction.

**2.2** **Indexed Families of Sets**

If we’re working with a few sets at a time, it’s probably sufﬁcient to use *A*, *B *, and *C *to represent them. Yet, if we have many sets, for instance, 10 sets (generally called a *family *or *collection *of sets instead of a set of sets), it might be more sensible to put them into a family and address them as *A*1 , *A*2 , …, *A*10 . In a case like this, we would say that the set {1*, *2*, *3*,…, *10} *indexes *the family of sets.

My friend (Ahmad Wachidul Kohar) and I try to make a resume and solve the exercises in those two sections which can be downloaded in this following link: *2.1 Proof Involving Sets and 2.2 Indexed Families of Sets*

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