Exam 1 Review

# Exam 1 Review - you, included with indexed families of sets...

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MAT 300, Mathematical Structures Spring 2010 Review for Exam 1 Exam 1 will consist of approximately 60% proofs and 40% related material. The break- down is as follows: (I) Deﬁnitions (5–10%). Be able to give proper mathematical deﬁnitions, as we have discussed in class, of the following concepts. Here, A and B are sets, and m and n are integers. In order to earn full credit your deﬁnition should introduce notation as needed and should be precise enough to use in proofs. (a) m divides n if (b) m is even if (c) m is odd if (d) A is a subset of B if (e) A = B if (f) The set A B = (g) The set A B = (h) The set A \ B = (i) The power set P ( A ) of a set A is (II) Short answer questions using logic, operations on sets, or true/false (30–35%). You should be able to (a) Negate a statement (see 2.2.2) (b) Decide logical equivalences (1.2.12, 1.5.10, 3.2.2) (c) Decide if a statement is true or false (2.1.7, 2.1.8, 2.2.3) (d) Give a counterexample if a statement is false (3.1.3, 3.1.16, 3.3.21) (e) Compute the intersection, union, or set complement with sets that are given to
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Unformatted text preview: you, included with indexed families of sets (see 2.3.6, 2.3.8). (III) Proofs (60%). Proofs you should be able to do are similar to proofs assigned as home-work. Know the dierence between the proof of a for every statement, which starts by making an arbitrary choice, and a there exists statement, where you start with scratch work to nd the answer. Know the dierence between direct proof, indirect proof, and proof by contradiction. Types of proofs: (a) Set containment or equality (see 3.1.8, 3.2.3, 3.3.2) (b) Logical equivalences (see 1.5.5, 2.2.7, 3.2.2) (c) Equalities or inequalities with real numbers (see 3.1.12, 3.2.7, 3.3.6) (d) Parity or divisibility of integers (see 3.3.18; also see the proof in lecture notes that an integer n is even if and only if n 2 is even.) 1...
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## This note was uploaded on 04/04/2010 for the course MAT 300 taught by Professor Thieme during the Spring '07 term at ASU.

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