UMBC CMSC203, Discrete Structures, Fall 2010

⇐ 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: 30 Sep 2010 15:33:27 EDT by Richard Chang
to Fall 2010 CMSC 203 Homepage