basic boolean rules can be referred to @ http://www.ee.surrey.ac.uk/Projects/Labview/boolalgebra/index.html#commutativelaw A'B + AB' + AB + A'B' = (A'B +A'B')+(AB'+AB) =A'(B+B')+A(B'+B) =A' (1) + A (1) = A' + A = 1 X' + XY + XZ' + XY'Z' X' + XY + XZ' (1+Y') X' + XY + XZ' X' + X(Y+Z') X' + Y + Z' [ T10 A]