Question

prove by the method of perfect induction( law of boolean algebra) , (A+B).(A'+B')=(A.B+A'.B')​

Answer 1

5. X . 0 =0
6. X . 1 =X
7. X . X =X
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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
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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




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Answer 2

Step-by-step explanation:

prove that x.x=0 by using prefect induction method