From 916f0248c4704299e21e0a9d6e592b7b371f3e13 Mon Sep 17 00:00:00 2001 From: Jan Meyer Date: Mon, 9 Mar 2026 18:27:32 +0100 Subject: [PATCH] vault backup: 2026-03-09 18:27:32 --- Counting.md | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) diff --git a/Counting.md b/Counting.md index 9c3573e..db44e9b 100644 --- a/Counting.md +++ b/Counting.md @@ -24,3 +24,21 @@ $$ #### Final calculation: Formula: $"Elements that are" x^2 + "Elements that are" x^5 - "Elements that are both"$ $==> 1,000 + 15 - 3 = 1,012$ + +## Type of Task: Boolean Lattice +Find the amount of upper bounds in ${0, 1}^5$ for the set of vectors $S = {x, y, z}$ +$$ +& x = (0, 1, 0, 0, 0) \ +& y = (0, 0, 1, 0, 1) \ +& z = (0, 1, 1, 0, 0) \ +$$ +> [!INFO] +> Method used is called **All-Zero Column Method** + +We look for columns that have $0$'s in all three vectors: Column $1$ and $4$, that's $2$ columns, so we define $k = 2$. +To get our result we calculate $2^k$ since there are only two possible states for each value $(0, 1)$: +$2^2 = 4$. +So we have **4** upper bounds in total. + +> [!INFO] +> For the amount of lower bounds we'd check for all-ones columns