UMBC CMSC203, Discrete Structures, Spring 2009

⇐ Proofs & English Indirect Proofs ⇒

Direct Proofs

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.

Example:

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.


QED
⇐ Proofs & English Indirect Proofs ⇒

Last Modified: 22 Jul 2024 11:28:07 EDT by Richard Chang
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