- (a4)
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A (B C) (A B} (A C) A (B C) (A B} (A C)
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(ligji distributiv)
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- (a5)
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A (B C) (A B} (A C), A (B C) (A B} (A C),
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(ligji distributiv)
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- P ë r k u f i z i m i 2.2.3. - Diferenca e bashkësive A, B quhet bashkësia e elementeue të bashkësisë A që nuk janë në bashkësinë B (fig. 1.4.), pra :
A\B {x x A X B}.
- Simboli \ (lexo: diferenca ose pa) është shenja e veprimit në fjalë.
- P.sh.:
\![{\displaystyle \scriptstyle {\mathbb {N} _{p}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f8a881acfc1827fff9c236c7d9978bac40ed5ff0) ![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , \![{\displaystyle \scriptstyle \mathbb {Z} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0c672518c0350ca035befd41c26633a2d399431) ![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , \![{\displaystyle \scriptstyle {\mathbb {N} _{c}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ef55c36254311f95c46fe04edacb561faf58514) ![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , {1,3,5,7}\{2,3,4,5} { 1, 7}.
- Në bazë të përkufizimit 2.2.3 del se A\A
![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) dhe A\![{\displaystyle \scriptstyle {\varnothing }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b81366d70c6c5b6e6679155c2449e11e4dae3f42) A, për çdo bashkësi A.
|
![](//upload.wikimedia.org/wikibooks/sq/thumb/0/0e/Diferenca_e_bashk%C3%ABsive_AB.PNG/260px-Diferenca_e_bashk%C3%ABsive_AB.PNG) Fig. 1.4.
|
![](//upload.wikimedia.org/wikibooks/sq/thumb/a/a7/Komplementi_i_bashk%C3%ABsis_B%28A%29.PNG/260px-Komplementi_i_bashk%C3%ABsis_B%28A%29.PNG) Fig. 1.5
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- Kur B
C, atëherë A\B quhet komplement i bashkësisë B ndaj bashkësisë A dhe shënohet CAB ose B' (fig. 1.5.).
- P.sh.:
![{\displaystyle \scriptstyle \mathbb {C} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe3a54bb4e56c039e18c3af24ba70ab377f7a07) ![{\displaystyle \scriptstyle \mathbb {Z} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0c672518c0350ca035befd41c26633a2d399431) ![{\displaystyle \scriptstyle \mathbb {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/40eac26c488d3257e3fbe63619729673145d228c) ![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) \![{\displaystyle \scriptstyle \mathbb {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/40eac26c488d3257e3fbe63619729673145d228c) {x x![{\displaystyle \scriptstyle \in }](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a4e4b18f88a540b881dab023807160f159f8a9) ![{\displaystyle \scriptstyle \mathbb {Z} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0c672518c0350ca035befd41c26633a2d399431) x<0}.
- Relacioni (A')'
A shpreh ligjin e involucionit.
- S h e m b u l l i 11. - Të vërtetohen relacionet:
(A B)' A' B' dhe (A B)' A' B'
- që paragesin ligjet e De Morganit.
- V ë r t e t i m : Të vërtetojmë relacionin e parë. Vërtetimi bëhet sipas skemës:
- (1) vërtetohet se (A
B)' A' B' ;
- (2) vërtetohet se A'
B' (A B)' ; dhe
- (3) nxirret konkludirni se (A
B)' A' B'.
- (1) vërtetimi i inkluzionit (A
B)' A' B'.
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