Question

Exercise 3.4.3: In Example 3.6, we developed the regular expression Use the distributive laws to develop two different, simpler, equivalent expres- sions.

Neatly with explanation please

Answer 1

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Answer)

Regular Expression: (0+1)*1(0+1) +  (0+1)*1(0+1)(0+1)

Regular Expression: (0 + 1) * 1 (0 + 1) + (0 + 1) * 1 (0 + 1) (0 + 1) Distributive Property (Distributive Law) a (b + c) = ab + ac a (b - c) = ab - ac After applying distributive law, the two different expression would be: 1) (0 + 1) * 10 + (0 + 1) * 11 + (0 + 1) * 1 (0 + 1) (0 + 1) 2) (0 + 1) * 1 (0 + 1) + (0 + 1) * 1 (0 + 1) 0 + (0 + 1) * 1 (0 + 1) 1

After applying distributive law, the two different expression would be:

1)

(0+1)*10 + (0+1)*11 + (0+1)*1(0+1)(0+1)

2)

(0+1)*1(0+1) + (0+1)*1(0+1)0 + (0+1)*1(0+1)1