UMBC CMSC203, Discrete Structures, Spring 2009
Direct proofs are given a name just to contrast them from the next
two proof methods: indirect proofs and proofs by contradiction. A
direct proof proceeds from the premises through some steps of logical
reasoning and arrives at the conclusion. For example, a direct proof
that a graph G can be colored using 4 colors would simply specify
the colors for each vertex in G and argue that none of the adjacent
vertices have been assigned the same color. A direct proof of an
implication, p ⇒ q, would assume p is true and argue directly
that q must also be true.
Claim: The graph below is 4-colorable.
Proof: Here is a 4-coloring of the graph. We leave it to
the reader to check that every pair of adjacent vertices (the
vertices connected by an edge) are colored with different colors.
12 Feb 2009 12:57:01 EST
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