Final Exam

  • Due Mar 21, 2023 at 11:59pm
  • Points 89
  • Questions 89
  • Available Mar 21, 2023 at 4pm - Mar 21, 2023 at 11:59pm 7 hours and 59 minutes
  • Time Limit 180 Minutes

Instructions

Set definitions

    • Positive integers: LaTeX: \textbf{Z}^{+} \triangleq \{1,2,...\} Z+≜{1,2,...}
    • Natural numbers: LaTeX: \textbf{N} \triangleq \{0,1,2,...\} N≜{0,1,2,...}

Propositional logic identities

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Valid inference rules for predicate logic

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Set identities

setidentities.png

Permutations, Combinations formulae

Generalized Product Rule

image-3.png

Permutations

image-1.png

Combinations (Subsets)image-2.png

Assignment problems formulae

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Pascal's identity

LaTeX: {n \choose k} = { {n-1} \choose {k-1} } + { {n-1} \choose k}(nk)=(n−1k−1)+(n−1k)

 

Graph vocabulary definitions

walk
A walk between vertices v1 and v2 is a connected sequence of vertices and edges beginning at v1 and ending at v2. The length of a walk is the number of edges in the sequence.
open and closed walks
An open walk is a walk between v1 and v2 where v1 LaTeX: \neq≠ v2.
A closed walk is a walk between v1 and v2 where v1 = v2.
trail
A trail is a walk with no repeated edges.
path
A path is a walk with no repeated vertices.
circuit
A circuit is a closed trail.
cycle
A cycle is a circuit of length 1 or more where no vertex is repeated except for the first and last.
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