From ac9d769b0a7bec1493578ce797e124dac81ece59 Mon Sep 17 00:00:00 2001 From: zacharias Date: Tue, 2 Sep 2025 17:00:02 +0200 Subject: [PATCH] sep-2-17_00 --- exercise-sep-2.txt | 7 +++++++ notes-sep-2.txt | 4 ++++ 2 files changed, 11 insertions(+) diff --git a/exercise-sep-2.txt b/exercise-sep-2.txt index fbb8fb0..0d866fd 100644 --- a/exercise-sep-2.txt +++ b/exercise-sep-2.txt @@ -13,3 +13,10 @@ AuB = {1, 2, 3, 5, 7, 9} A↓uB = {3, 7} A\B = {1, 9} A"delt"B = {1, 2, 5, 9} + + +Beviska: +1) ¨A↓u(AuB) = B\A + +2) (AuB)↓u¨(A↓uB) = (A↓u¨B)u(B↓u¨A) + diff --git a/notes-sep-2.txt b/notes-sep-2.txt index fc839e2..f0d9014 100644 --- a/notes-sep-2.txt +++ b/notes-sep-2.txt @@ -19,3 +19,7 @@ Räkne regler: x € ¨(AuB) => x !€ AuB => {x !€ A, x !€ B => x !€ {x € ¨A, x € ¨B => x € ¨(AuB). Visar att ¨(AuB) …c A↓uB. x € ¨A↓u¨B => {x € ¨A, x € ¨B => {x !€ A, x !€ B => x !€ AuB => x € ¨(AuB). Visar att ¨A↓uB …c ¨(AuB). Resultat: ¨(AuB) = ¨Au¨B +- Distributiv: (AuB)↓uC <=> (A↓uC)u(B↓uC), (A↓uB)uC <=> (AuC)↓u(BuC) +- Absorbering: A↓u(AuB) = A, Au(A↓uB) = A +- Differens: A\B <=> A↓u¨B +