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Jan Meyer
2026-03-09 18:27:32 +01:00
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Counting.md
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@@ -24,3 +24,21 @@ $$
#### Final calculation: #### Final calculation:
Formula: $"Elements that are" x^2 + "Elements that are" x^5 - "Elements that are both"$ Formula: $"Elements that are" x^2 + "Elements that are" x^5 - "Elements that are both"$
$==> 1,000 + 15 - 3 = 1,012$ $==> 1,000 + 15 - 3 = 1,012$
## Type of Task: Boolean Lattice
Find the amount of upper bounds in ${0, 1}^5$ for the set of vectors $S = {x, y, z}$
$$
& 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