12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Wednesday April 09, 2025
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)
Revision as of 16:04, 14 March 2010
, 16:04, 14 March 2010→Majority function
Line 191:
Line 191:
Here's a nice example that was posted as a [http://mathoverflow.net/questions/9292/newbie-boolean-algebra-question question at MathOverFlow].+
+
+<br>+
|}
|}
−====Majority function====
+====Majority function example====
−A reader posed a [http://mathoverflow.net/questions/9292/newbie-boolean-algebra-question question] at [http://mathoverflow.net/ MathOverFlow] asking for a proof of the following equation in boolean algebra:
+{| align="center" cellpadding="10"
+|
+<math>\begin{matrix}
+a b \bar{c} + a \bar{b} c + \bar{a} b c + a b c
+\\[6pt]
+\iff
+\\[6pt]
+a b + a c + b c
+\end{matrix}</math>
+|}
+=====Proof 1 : Storyboard=====
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
Line 236:
Line 249:
|}
|}
−=====Proof 1 : Animation=====
Here's a rough animation of the graphical transformations in the above proof:
Here's a rough animation of the graphical transformations in the above proof:
