Question

using perfect induction method
x+xy=X+y​

Answer 1

Answer:

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Explanation:

5. X . 0 =0

6. X . 1 =X

7. X . X =X

__

8. X . X =0

==

9. X = X

Boolean Algebra

16. X + XZ = X

17. X(X+Z)=X

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18. X+ X Y =X+Y

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19. X ( X +Y) =X.Y

____ __ __

20. X+Y = X . Y

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21. X.Y =X+Y

Laws of absorption Identity Theorems

De Morgan's Theorems

262

AND operations

Double complement

10. X + Y = Y + X

11. XY=YX

12. (X + Y ) +Z = X +(Y + Z) Associative laws

13. (X . Y). Z =X. (Y. Z)

14. X (Y + Z) = XY + XZ Distribution Law

15. X + Y .Z = (X + Y) . (X + Z) Dual of Distributive Law

Commutative laws

Proof of Boolean Algebra Rules:

Every rule can be proved by the application of rules and by perfect Induction.

Rule 15:

(i) This rule does not apply to normal algebra We follow:

(X + Y) (X + Z) = XX + XZ +YX + YZ

=X+ XZ +YX + YZ, X.X=X

Answer 2

Answer:

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