## A Brief Review of Set Theory

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?...

January 11, 2021 · 14 min · Adam Thompson

## Boolean Algebra Cheat Sheet

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

April 20, 2020 · 1 min · Adam Thompson

## Logic Rules Cheat Sheet

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....

February 2, 2020 · 2 min · Adam Thompson