1. Докажите тождества:

1. X ∪  Z ∪ X

∩

X ∩∪ Z |  Z |

Y | (∪ Z)  ;

1)X∩Y∩(X∩Z∪X∩Y∩Z∪Z∩t)X∩Y∩Z

Y∪∪

(X | (X | ))∪(|(|)) 

∩(| X∪) ;

₂₎ ∩Y∩Z∪X∩Z(X∪Y) ∩Z

X∪∪X∪Z∪

Y| (Y|X∪)Y∩X

(∩|X) |;

3)X∩Y∪X∩Y∩Z∪X∩Y∩Z∪X∩Y∩ZX∩Y

X ∩ ∩ Y

(X | )|  X

(X∩) | (∪) ;

₄₎ ∪ Y ∩Z ∪ ∪ ∪ U

∩∩

| Z | Y

 ;

5)((X∪Y)∪(∩)) ∩X∩

 (∪Z) ∩

X|Y∪X∩ZX|Y∩

 ;

₆₎ U

X ∩ Y

| X ∩ ∩ Y

∩(Y ∪ Z) ∩ X ∩Y ;

7)(X∪Y∪Z) ∩ (X∪Y)∪ZX∪Z∪Y

∪

Y| (X∩Y|)Y|X

| ∪Y ;

8)X ∪∪ X ∩ Z  U

∪∪

X ∪ ∩ (Y|)X

| ∪ ;

9)(X∪Z) ∩ (X∪Y) ∩ (Y∩Z)Y∩Z

∩ (Y∪) ∩

(|) |X|Z

∩ ;