MAT 309 Discrete Structures

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MAT 309Discrete Structures

• Chapter Two
• Sets, Functions and Sequences

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Sets and Subsets

• A?B ? ?a (a?A?a?B)
• A?B ? A?B and ?b (b?B and b?A)
• A number of elements in set A
• AxB Cartesian Product
• AxB (a,b) a?A and b?B

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Special Sets

• Empty Set
• Power Set, P(A)
• P(A) 2A
• Universal Set U
• Partition

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Set Properties

• Theorem 2.1-12, page 82
• Associative laws
• Commutative laws
• Distributive laws
• Identity laws
• Complement laws
• Idempotent laws
• Bound laws
• Absorption laws
• Involution laws
• DeMorgans laws

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Functions

• Modulus Operator x mod y remainder when x is
  divided by y
• Ex ISBN check digit
• Ex Hash functions
• Ex Pseudorandom numbers
• Ex Floor
• Ex Ceiling

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Function PropertiesfA ?B

• One to One
• a?b ? f(a) ?f(b)
• f(a)f(b) ? ab
• Onto
• b?B ? ?a?A, f(a)b
• Bijection
• 1-1 AND onto

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Functions

• Inverse
• Composition
• Binary Operation
• Unary Operation

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Sequences and Series

• Explicitly or Recursively Defined
• Increasing, Decreasing
• Subsequence
• String a finite sequence of characters
• Catenation
• Substring