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Wednesday, April 28, 2021, 8:04 PM, , COMBINED ISC 135 Page 1

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Simplify using the laws of Boolean Algebra. At each step, state clearly the law used for simplification., (i) A. (B.C)’ + (A.B.C)’, (ii) A.B+A’.C+B.C, (iii) A.[B+C.(A.B+A.C)’], (iv) (A+B’).(B+CD)’, (v) ((P’+Q) . (Q’+R))’ +(P’+R), (vi) AB + (AC)’ +AB’C, (vii) ((AB)’+A’+AB)’, (viii) X’YZ+XY’Z+XYZ+XYZ’, (ix) Z . ( Z + X ) X ( Y + Y ), (x) AB+(AC)’+AB’C(AB+C), (xi) X.Y. ( X.Y+ Y.Z ), (xii) A.B.D + A.B.C.D +A.B.D + A.B.C.D, (xiii) X’.Y’.Z’ + X’.Y’.Z + X’Y.Z + X’.Y.Z’ + X.Y’.Z + X.Y’Z, (xiv) X’Y + YZ + XZ, (xv) X.(X’+Y’) + (Z+X) + (Z’+Y), (xvi) A’B + AB’C + A, (xvii) [(p’+q).(q’+r)]’+(p’+r), (xviii) XY’ (X’ YZ+X(YZ)’+ ( XY)’Z), , COMBINED ISC 135 Page 8

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(xvii) [(p’+q).(q’+r)]’+(p’+r), (xviii) XY’ (X’ YZ+X(YZ)’+ ( XY)’Z), (xix) (A,B)’ + (A.C)’ + A’ + A’.C’, (xx) AB + (AC)’ +AB’C, (xxi) X’Y’Z’ + XYZ’ + XY’Z’ + X’YZ’, (xxii) C.D’ + A + A + C’.D’ + A.B, (xxiii) z . ( z + x ) x ( y + y ), (xxiv) (A.B’+A.B)(A+B), (xxv) (A,B)’ + (A.C)’ + A’ + A’.C’, , 8. Verify the following:, (i) X’. Y.Z + X.Y’.Z + X.Y.Z’ + X.Y.Z = X.Y + Y.Z + Z.X, (ii) ((P’ + Q).(Q’ + R))’ + (P’ + R) = 1, (iii) X’. Y.Z + X.Y’.Z + X.Y.Z’ + X.Y.Z = X.Y + Y.Z + Z.X, (iv) X+Y.Z=(X+Y)(X+Z), (v) (A+B).(A’+C) = (A+B+C).(A+B+C’).(A’+B+C).(A’+B’+C), , A. (B.C)’ + (A.B.C)’, , A.B+A’.C+B.C, , A.[B+C.(A.B+A.C)’], , ((P’+Q) . (Q’+R))’ +(P’+R), , ((AB)’+A’+AB)’, , (A+B’).(B+CD)’, , AB + (AC)’ +AB’C, , X’YZ+XY’Z+XYZ+XYZ’, COMBINED ISC 135 Page 9

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X’YZ+XY’Z+XYZ+XYZ’, , ((AB)’+A’+AB)’, , Z.(Z+X)X(Y+Y), , (A.B’+A.B)(A+B), , (A.B)’ + (A.C)’ + A’ + A’.C’, , XY’ (X’ YZ+X(YZ)’+ ( XY)’Z), , (A+B).(A’+C) = (A+B+C).(A+B+C’).(A’+B+C).(A’+B’+C), , X+Y.Z=(X+Y)(X+Z), , COMBINED ISC 135 Page 10