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Unformatted text preview: MAT 300, Mathematical Structures Spring 2010 Review for Exam 2 Exam 2 covers problem sets 57, and includes material from sections 3.4, 3.5, 3.6, 4.1, 6.1, 5.1, and 5.2. Material from earlier sections is included as needed. Be sure to check your homework solutions against my posted solutions. The exam will consist of approximately 60% proofs and 40% related material. The breakdown is as follows: (I) Definitions (1020%). Be able to complete the following mathematical definitions. Here, A , B , and C are sets, and f : A B and g : B C are functions. In order to earn full credit your definition should introduce notation as needed and should be precise enough to use in proofs. (a) The Cartesian product A B of sets A and B is: the set of all ordered pairs ( a, b ) where a A and b B . (b) The sets A and B are disjoint if: A B = . Equivalently, (b ) The sets A and B are disjoint if: for all x , x / A or x / B ....
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