文档介绍：Proof Templates
1 Direct proof of an if-then theorem. 19
2 Direct proof of an if-and-only-if theorem. 23
3 Refuting a false if-then statement via a counterexample. 26
4 Truth table proof of logical equivalence. 30
5 Proving two sets are equal. 51
6 Proving one set is a subset of another. 54
7 Proving existential statements. 59
8 Proving universal statements. 60
binatorial proof. 67
10 Using inclusion-exclusion. 129
11 Proof by contrapositive. 136
12 Proof by contradiction. 137
13 Proving that a set is empty. 140
14 Proving uniqueness. 140
15 Proof by smallest counterexample. 146
16 Proof by the Well-Ordering Principle. 150
17 Proof by induction. 158
18 Proof by strong induction. 163
19 To show f : A ~ B. 196
20 Proving a function is one-to-one. 199
21 Proving a function is onto. 201
22 Proving two functions are equal. 213
23 Proving (G, *) is a group. 344
24 Proving a subset of a group is a subgroup. 354
25 Proving theorems about trees by leaf deletion. 418
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