need help with simplifing ab'c(bd+cde)+ac'. book answer indicates a(c'+b'de) i get a(c'+b'cde). need some help
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Both answers are correct, but obviously the book answer is shorter. To show that they are equivalent, it is sufficient to show that c'+b'de = c'+b'cde. Viewed more abstractly, it is sufficient to show that x + y = x + yx' (substitute x = c' and y = b'de). Indeed,
x + y = x + y1 = x + y(x + x') = x + yx + yx' = 1x + yx + yx' = (1 + y)x + yx' = 1x + yx' = x + yx'.