Proofs

In discrete mathematics and functional programming, writing proofs involve "justifying everything." As a result, proofs can become complicated and colorful. In order to become comfortable at writing proofs, one must understand the basic structure and writing of a proof. Fortunately, in Thomas VanDrunen's Discrete Mathematics and Functional Programming, there are many proof templates that are used to prove a variety of theorems. Each template focuses on a particular technique, such as set theory or the property of functions. This is advantageous in order to build an arsenal of techniques and tools that could be used to proof theorems. As you progress further in the book, proofs become more difficult and require more than one technique to write them. On a final note, writing proofs is like solving a problem. There is exists more than one path to the solution. Therefore, do not be discouraged if the solutions given here do not match your own. As Mr. VanDrunen will say, "Let us march and dance."

Write the first section of your page here.

SET PROOFS

 * 1) SUBSETS
 * 2) SET EQUALITY
 * 3) SET EMPTINESS
 * 4) CONDITIONAL PROPOSITIONS
 * 5) BICONDITIONAL PROPOSITIONS

QUANTIFICATION

 * 1) UNIVERSALLY QUANTIFIED PROPOSITIONS
 * 2) EXISTENCE
 * 3) NONEXISTENCE
 * 4) UNIQUENESS
 * 5) UNIQUE EXISTENCE

RELATION PROPERTIES

 * 1) REFLEXIVITY
 * 2) SYMMETRY
 * 3) TRANSITITY
 * 4) ANTISYMMETRY