Ütjsaagenloogik

Tekst üüb Öömrang

Ütjsaagenloogik as en dial faan't loogik. Hat befaadet ham mä reegeln, hün wäärs ferbünjen ütjsaagen haa.

Ianfach ütjsaagen san woor (w) of ferkiard (f).

• ${\displaystyle A_{1}}$: 12 könst dü troch 3 dial. (w)
• ${\displaystyle A_{2}}$: Arke auto as green. (f)

• ${\displaystyle \neg A_{1}}$: 12 könst dü ei troch 3 dial. (f)
• ${\displaystyle \neg A_{2}}$: Diar as ei arke auto green. (At jaft tumanst ian auto, diar ei green as.) (w)

För an-ferbinjangen jaft at jodiar skriiw- an spreegwiisen:

• Spreegwiis: A an B
• Skriiwwiis: ${\displaystyle A\land B}$
• uun a technik uk: A AND B

${\displaystyle A}$	${\displaystyle B}$	${\displaystyle A\land B}$
woor	ferkiard	ferkiard
woor	woor	woor
ferkiard	ferkiard	ferkiard
ferkiard	woor	ferkiard

Bispal

A: 12 könst dü troch 3 dial
B: 12 as en kwadroottaal

• ${\displaystyle C_{1}}$: 12 könst dü troch 3 dial an 12 as en kwadroottaal.
• ${\displaystyle C_{2}}$: 12 könst dü troch 3 dial an 12 as nian kwadroottaal.
• ${\displaystyle C_{3}}$: 12 könst dü ei troch 3 dial an 12 as en kwadroottaal.
• ${\displaystyle C_{4}}$: 12 könst dü ei troch 3 dial an 12 as nian kwadroottaal.

Bluas ${\displaystyle C_{2}=A\land B}$ as woor, auer ${\displaystyle A}$ woor as an uk ${\displaystyle B}$ woor as.

För of-ferbinjangen jaft at jodiar skriiw- an spreegwiisen:

• Spreegwiis: A of B, mend as: A of B of A an B, flooksis uk: A an/of B
• Skriiwwiis: ${\displaystyle A\lor B}$
• uun a technik uk: A OR B

${\displaystyle A}$	${\displaystyle B}$	${\displaystyle A\lor B}$
woor	ferkiard	woor
woor	woor	woor
ferkiard	ferkiard	ferkiard
ferkiard	woor	woor

Bispal

A: 12 könst dü troch 3 dial
B: 12 as en kwadroottaal

• ${\displaystyle C_{1}}$: 12 könst dü troch 3 dial of 12 as en kwadroottaal.
• ${\displaystyle C_{2}}$: 12 könst dü troch 3 dial of 12 as nian kwadroottaal.
• ${\displaystyle C_{3}}$: 12 könst dü ei troch 3 dial of 12 as en kwadroottaal.
• ${\displaystyle C_{4}}$: 12 könst dü ei troch 3 dial of 12 as nian kwadroottaal.

${\displaystyle C_{1}=A\lor B}$, ${\displaystyle C_{2}=A\lor B}$ an ${\displaystyle C_{4}=A\lor B}$ san woor, auer tumanst ian ütjsaag faan ${\displaystyle A}$ of ${\displaystyle B}$ woor as.

Bluas ${\displaystyle C_{3}=A\lor B}$ as ferkiard, auer neder A of B woor san.

För implikatjuunen jaft at jodiar skriiw- an spreegwiisen:

${\displaystyle A\rightarrow B}$

(of uk ${\displaystyle B\subset A}$; det koon oober ferwakselt wurd mä't tiaken för dialmengden!)

• Ütj A fulagt B
• Wan A, do B
• Saner B nian A

A woort uk antezedens näämd, an B sukzedens of konsekwens

${\displaystyle A}$	${\displaystyle B}$	${\displaystyle A\rightarrow B}$	${\displaystyle \neg B\rightarrow \neg A}$	${\displaystyle \neg A\lor B}$
woor	woor	woor	woor	woor
woor	ferkiard	ferkiard	ferkiard	ferkiard
ferkiard	woor	woor	woor	woor
ferkiard	ferkiard	woor	woor	woor

Bispal

A - At rinjt
B - A struat as wiat

• ${\displaystyle C_{1}}$: Wan't rinjt, as a struat wiat. (w)
• ${\displaystyle C_{2}}$: Wan't rinjt, as a struat ei wiat. (f)
• ${\displaystyle C_{3}}$: Wan't ei rinjt, as a struat wiat. (mei wees, w)
• ${\displaystyle C_{4}}$: Wan't ei rinjt, as a struat ei wiat. (mei wees, w)

Jodiar tuupsaat ütjsaagen san likwäärdag (ekwiwalent), auer jo leewen di salew wäärs uun woorhaidstoofel haa:

Wan't rinjt, as a struat wiat (${\displaystyle A\rightarrow B}$).

Wan a struat ei wiat as, koon't ei riin (${\displaystyle \neg B\rightarrow \neg A}$).

At hää ei rinjd, of a struat as wiat (${\displaystyle \neg A\lor B}$).

${\displaystyle A}$	${\displaystyle B}$	${\displaystyle A\leftrightarrow B}$	${\displaystyle (A\rightarrow B)\land (B\rightarrow A)}$
woor	woor	woor	woor
woor	ferkiard	ferkiard	ferkiard
ferkiard	woor	ferkiard	ferkiard
ferkiard	ferkiard	woor	woor

At bikonditjunaal woort so skrewen an spreegen:

${\displaystyle A\leftrightarrow B}$

• A jüst do an bluas do, wan B
• B jüst do an bluas do, wan A
• A an B san ekwiwalent

Bispal

A - Daalang as teisdai
B - Maaren as wäärnsdai

Uun steed faan ${\displaystyle A\leftrightarrow B}$ könst dü uk sai, ütj A fulagt B an ütj B fulagt A: ${\displaystyle (A\rightarrow B)\land (B\rightarrow A)}$.

${\displaystyle A}$	${\displaystyle B}$	${\displaystyle \neg (A\leftrightarrow B)}$	${\displaystyle A{\dot {\lor }}B}$
woor	woor	ferkiard	ferkiard
woor	ferkiard	woor	woor
ferkiard	woor	woor	woor
ferkiard	ferkiard	ferkiard	ferkiard

At kontrawalens woort so skrewen of spreegen:

${\displaystyle \neg (A\leftrightarrow B)}$.

${\displaystyle A{\dot {\lor }}B}$

uun a technik uk: A XOR B

• A an ei B
• B an ei A
• Genau ian faan A of B

Wikibooks: Ütjsaagenloogik (sjiisk)

• Mengdeliar