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Prove LHS=RHS in  A + ĀB = A +B using theorems and laws of Boolean Algebra.

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$A + A'B = A+B$

 

$LHS:$

 

$A.1 + A'B$

 

$A(1+B) + A'B$                $\because \  1 + x = 1 [using \ OR \ property]$

 

$A+AB + A'B$

 

$A+(A + A')B$

 

$A + B$                           $\because \  x + x' = 1 [using \ OR \ property]$   

 

$LHS = RHS$
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