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Boolova algebra

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Logika vs Algebra<br />

komutatívnosť<br />

asociatívnosť<br />

distributívnosť<br />

de Morganove<br />

zákony<br />

idempotentnosť<br />

identita<br />

absorbcia<br />

involúcia<br />

zákon vylúčenia<br />

tretieho<br />

zákon sporu<br />

<strong>algebra</strong> množín<br />

A∩B=B∩A<br />

A∪B=B∪A<br />

A∩B∩C = A∩B∩C<br />

A∪B∪C = A∪B∪C<br />

A∩ B∪C = A∪B∩ A∪C<br />

A∪ B∩C = A∩B∪ A∩C<br />

A∩B=A∪B<br />

A∪B=A∩B<br />

A∩A=A<br />

A∪A=A<br />

A∩U = A<br />

A∪∅=A<br />

¬ A∩∅=∅<br />

A∪U =U<br />

A=A<br />

A∪A=U<br />

A∩A=∅<br />

výroková logika<br />

p∧q≡q∧ p<br />

p∨q≡q∨ p<br />

p∧q∧r≡ p∧q∧r<br />

p∨q∨r≡ p∨q∨r<br />

p∧q∨r ≡ p∨q∧ p∨r<br />

p∨q∧r ≡ p∧q∨ p∧r<br />

¬ p∧q≡¬ p∨¬q<br />

¬ p∨q≡¬ p∧¬q<br />

p∧ p≡ p<br />

p∨ p≡ p<br />

p∧1≡ p<br />

p∨0≡ p<br />

p∧0≡0<br />

p∨1≡1<br />

¬¬ p≡ p<br />

p∨¬ p≡1<br />

p∧¬ p≡0

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