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Explanation:
Dual of an expression requires interchanging
+ with .
. with +
0 with 1
1 with 0
41. A + A'B = (A+A')(A+B) = 1.(A+B) = A+B
dual of A+B = AB
complemlement of an expression E is E'. Before complementing simplify the expression.
42. A'(BC'+BC) = A'B(C'+C) = A'B as C'+C = 1
complemlement of the above expression= (A'B)' = (A')'+ B' = A+B'
43. complement of AB'+C'D' = (AB'+C'D')' = (AB')'(C'D')' = (A'+B)(C+D)
44. X'Y'+XY'Z = Y'(X'+XZ) = Y'(X'+X)(X'+Z) = Y'(X'+Z)
complement of the above expression= (Y'(X'+Z))' = (Y')'+(X'+Z)' = Y+((X')'Z') = Y+XZ'
45. XY+Y'Z+ZZ'=XY+Y'Z as ZZ'=0
complement of the above expression= (XY+Y'Z)' = (XY)' (Y'Z)' = (X'+Y')(Y+Z')
46. X+XY'+X'Z' = X(1+Y')+X'Z' = X+X'Z = (X+X')(X+Z) = 1(X+Z) = X+Z
complement if the above expression = (X+Z)' = X'Z'
Answer:
above answer is correct