Set theory is the branch of mathematics that, unsurprisingly, deals with sets. It’s an area of great importance in a number of fields, including computer science. In this post, I’ll go over a brief review of basic set theory as it pertains to those pursuing an interest in computer science. Let’s just jump right in! What is a Set? The first and most logical question we can answer about set theory is just what is a set?...
I previously posted a logic rules cheat sheet and figured it was about time that I do the same for boolean algebra. Expression Equivalent To Name of the Rule $$ X + Y $$ $$ Y + X $$ Commutative $$ X \cdot Y $$ $$ Y \cdot X $$ Commutative $$ (X + Y) + Z $$ $$ X + (Y + Z) $$ Associative $$ (X \cdot Y) \cdot Z $$ $$ X \cdot (y \cdot Z) $$ Associative $$ X + (Y \cdot Z) $$ $$ (X + Y) \cdot (Z + Z) $$ Distributive $$ X \cdot (Y + Z) $$ $$ (X \cdot Y) + (X \cdot Z) $$ Distributive $$ X + 0 $$ $$ X $$ Identity $$ X \cdot 1 $$ $$ X $$ Identity $$ X + X' $$ $$ 1 $$ Complement $$ X \cdot X' $$ $$ 0 $$ Complement $$ X + X $$ $$ X $$ Idempotence $$ X \cdot X $$ $$ X $$ Idempotence
When working with logic in discrete math appliations there are a plethora of rules you can use for working with the well formed formulas. Remembering them all can be a daunting task, which is why I like to have a cheat sheet available. As such, here’s a simple one that I like to use when working with these problems. Equivalence Rules Expression Equivalent To Name of the Rule $$ P \lor Q $$ $$ Q \lor P $$ Commutative - comm....