From Truth Table to DNF or CNF
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when someone needs a concrete, step-by-step method for converting a logical expression or truth table into a normal form.
Recommended by 3 people across 3 different months, 2012 to 2018.
What it is
A 12-minute walkthrough from the sergiouniversity channel showing how to turn a truth table into disjunctive normal form (DNF) or conjunctive normal form (CNF). It works through the mechanical procedure of reading off rows of the table and combining atoms with AND and OR.
What people said
Recommends Charles Stewart · 2012-11 · Mathematics Stack Exchange · on “Is the associative property of XOR provable or axiomatic?”
@trideceth12: The best I saw was a YouTube video - you have to watch over 3 minutes to see what is going on, so maybe a question here is more useful. Link - [this video]
Recommends snepp · 2016-12 · Mathematics Stack Exchange · on “Can simple logic conditions be created from nested complex conditions”
It seems I want a "normal form". I still not sure what is the name of the normal form which does not have parenthesis, I am looking at this [this video] Thank you.
Recommends Charlie Parker · 2018-10 · Mathematics Stack Exchange · on “Find DNF and CNF of an expression”
For DNF: look at each row where $p = 1$ encode a proposition from the atoms $p_i$ for row $i$ (that gives $p$ is 1) that has $a_i$ if that atom is 1 in the truth table and $\neg a_i$ if it's 0. You are using an and to combine the atoms so that only this terms is 1 when you are on that row. You can think of this conjunction as a product. take the OR of all such proposition corresponding to the rows being 1 since this proposition is a disjunction (think of it as an addition) that are only 1s for unique rows, you get the whole thing is only 1 when you need it to be 1. For CNF: Look at the rows where $p=0$ encode a proposition from the atoms $p_i$ for row $i$ (that gives p being zero) that has $