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Write duals of the following expressions :

(i)  1 + x =1

(ii)  (a + b).(a’ + b’)

(iii)  ab + bc = 1

(iv)  (a’c + c’a)(b’d + d’b)

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(i)  0 . x = 0

(ii)  ab + a’b’

(iii)  (a + b)(b + c) = 0

(iv)  ((a’+ c)(c’ + a)) + ((b’+ d)(d’ + b)) 

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