21. Составив таблицы истинности, выясните, равносильны ли следующие формулы алгебры высказываний:

№

1

F(X,Y,Z) = [ X↔((YZ) → (XY)) ]

G(X,Y,Z) = ((XZ)(XZ))Y

2

F(X,Y,Z) = ((X→ØY)ÚZ) Ù (Ø(XÙY)↔ØZ)

G(X,Y,Z) = (XÙYÙZ)Ú((X→ØY)ÙØZ)

3

F(X, Y, Z) = ((X(YZ))X)( (XY) Z);

G(X, Y, Z) = X(YZ).

4

F(X, Y, Z) = ((X^(Y¦Z)) ¬(X ¬ Z))1 ¬ (¬Y1 Z)

G(X, Y, Z) = ¬(X ¦Z) Y

5

F(X, Y, Z) = ¬ [((¬Y ۷ ¬Z)↔X)۸(¬X۸(Y→ ¬Z))]

G(X, Y, Z) = (X۸Y۸Z) ۷ ¬X ۷ (X۸ ¬Y) ۷ (X۸Y۸ ¬Z)

6

F(X,Y,Z) =

G(X,Y,Z) =

7

8

F(X, Y, Z) = ­­­­

G(X, Y, Z) =

9

10

F(X, Y, Z) = ^┐[ ^┐ X ↔ ((Y V ^┐Z) → ^┐(X V ^┐Y))]

G(X, Y, Z) = ((^┐X^┐Z) V (XZ))^┐Y

11

12

13

F(X,Y,Z) = ( (X↔(YZ)) X)→( (XY)↔Z)

G(X,Y,Z) = X(Y↔ Z)

14

F(X, Y, Z) = ((X٨(Y→Z)) ٧¬(X٧¬Z)↔( ¬Y↔Z)

G(X, Y, Z) = ¬(X→Z) ٧Y

15

F(X,Y,Z) = [ X↔((YZ) → (XY)) ]

G(X,Y,Z) = ((XZ)(XZ))Y

16

F(X,Y,Z) = ((X→ØY)ÚZ) Ù (Ø(XÙY)↔ØZ)

G(X,Y,Z) = (XÙYÙZ)Ú((X→ØY)ÙØZ)

17

F(X, Y, Z) = ((X(YZ))X)( (XY) Z);

G(X, Y, Z) = X(YZ).

18

F(X, Y, Z) = ((X^(Y¦Z)) ¬(X ¬ Z))1 ¬ (¬Y1 Z)

G(X, Y, Z) = ¬(X ¦Z) Y

19

F(X, Y, Z) = ¬ [((¬Y ۷ ¬Z)↔X)۸(¬X۸(Y→ ¬Z))]

G(X, Y, Z) = (X۸Y۸Z) ۷ ¬X ۷ (X۸ ¬Y) ۷ (X۸Y۸ ¬Z)

20

F(X,Y,Z) =

G(X,Y,Z) =

21

22

F(X, Y, Z) = ­­­­

G(X, Y, Z) =

23

24

F(X, Y, Z) = ^┐[ ^┐ X ↔ ((Y V ^┐Z) → ^┐(X V ^┐Y))]

G(X, Y, Z) = ((^┐X^┐Z) V (XZ))^┐Y

25

26

27

F(X,Y,Z) = ( (X↔(YZ)) X)→( (XY)↔Z)

G(X,Y,Z) = X(Y↔ Z)

28

F(X, Y, Z) = ((X٨(Y→Z)) ٧¬(X٧¬Z)↔( ¬Y↔Z)

G(X, Y, Z) = ¬(X→Z) ٧Y

№

1

((P→Q)(R→S)(P R)) → (Q S)

2

((P→R)Ù(Q→S)Ù(¬RÚ¬S))→(¬PÚ¬Q)

3

((PQ) (RS)(PR)) (QS).

4

((P¦R) ^ (Q¦S) ^ (¬ R ¬ S))¦(¬P¬Q)

5

(P→Q)→{(R→ ¬Q)→[((S→ ¬P)→R)→((¬T۷P)→(T→S))]}

6

7

8

9

10

((( PQ)→ R)(^┐R→ Q)) → (P→ R)

11

12

13

((P→R)(Q→S)(R VS)) → (P VQ)

14

(P→Q) →{(R→¬Q) →[((S→¬P) →R) →((¬T٧P)→(T→S))]}

15

((P→Q)(R→S)(P R)) → (Q S)

16

((P→R)Ù(Q→S)Ù(¬RÚ¬S))→(¬PÚ¬Q)

17

((PQ) (RS)(PR)) (QS).

18

((P¦R) ^ (Q¦S) ^ (¬ R ¬ S))¦(¬P¬Q)

19

(P→Q)→{(R→ ¬Q)→[((S→ ¬P)→R)→((¬T۷P)→(T→S))]}

20

21

22

23

24

((( PQ)→ R)(^┐R→ Q)) → (P→ R)

25

26

27

((P→R)(Q→S)(R VS)) → (P VQ)

28

(P→Q) →{(R→¬Q) →[((S→¬P) →R) →((¬T٧P)→(T→S))]}