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State and Prove Idempotent law algebraically??

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Idempotent Law – An input that is AND´ed or OR´ed with itself is equal to that input   

A + A = A    A variable OR’ed with itself is always equal to the variable 

A . A = A    A variable AND’ed with itself is always equal to the variable

Proof: 

x + x = (x + x) • 1  (1 is the identity for AND)

= (x + x) • (x + x')   (Complement, x + x' = 1) 

= x + (x • x')    (OR distributes over AND) 

= x + 0    (Complement, x • x' = 0)

= x        (0 is the identity for OR) 

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