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LastRevHmwk120304

LastRevHmwk120304 - REVIEW SHEET You already have the...

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REVIEW SHEET 12/1/04 You already have the previous two review sheets. This review sheet covers material since second midterm. DEFINITIONS: 1. , , , {x}, {x 1 ,...,x n }, {x|P(x)}, {x A|P(x)}. 2. Proper subset, A = B, , , -, c . 3. Disjoint, mutually disjoint, partition. 4. Power set, ordered pairs, ordered tuples, Cartesian products. 5. Relation from A to B. x R y. Arrow diagram for relation. 6. Inverse of a relation, R-1. Functions as relations. Directed graph of a relation. 7. f:A Æ B. domain of a function. range of a function. co- domain of a function. Inverse image of a point under a function. 8. f = g. i A . Sequences as functions. 9. f is one-one. f:A Æ B is onto. f:A Æ B is a bijection. Inverse of a bijection. gof (when well defined). THEOREMS (know full statements): 1. Existence and uniqueness of binary integer representations. 2. Well ordering principle for the integers. 3. Cardinality of power set of finite sets. 4. Composition of one-one functions is one-one. Composition of onto functions is onto. Composition of bijections is a bijection.

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