simplify the following boolean function using boolean laws :- (X+Y).(X.Z+Z).(Y'+X.Z)'

Question

(X+Y).(X.Z+Z).(Y'+X.Z)'

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

(X + Y).(X.Z + Z).(Y' + X.Z)'

= (X + Y).((X+1).Z).((Y')' + (X.Z)') (∵ (A + B)' = A' + B' and (A+B).C = A.B + A.C)

= (X + Y).(1.Z).(Y + (X'+Z'))(∵ A+1 = 1,(y')' = y and (A.B)' = A' + B')

= (X + Y).Z.(Y + (X'+Z'))(∵ 1.Z = Z)

= (X + Y).(Y.Z + (X'+Z')) (∵ A.B = B.A)

= (X + Y). (Y.(ZX'+Z.Z')) (∵ A.(B+C) = A.B + A.C)

= (X + Y).(Y. (ZX' + 0) (∵ Z.Z' = 0)

= (X + Y).Y.(ZX') (∵ A+0 = A and A.(B.C) = (A.B).C = A.B.C)

= (XY + Y.Y) (ZX') (∵ (A+B).C = A.C + B.C)

= (XY + Y).(ZX') (∵ Y.Y =Y)

= (X+1).Y. ZX' (∵ (X+1).Y = XY +Y)

= (1.Y).ZX' (∵ X+1 = 1)

= Y.ZX' (∵ 1.Y = Y)

simplify the following boolean function using boolean laws :- (X+Y).(X.Z+Z).(Y&#39;+X.Z)&#39;