I know that (1 + 0)* is the set of all bit strings; but isn't 1* + 0* the same thing?
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1$\begingroup$ The second one is "all ones or all zeroes", which doesn't include e.g. 0101010 $\endgroup$– vonbrandCommented Feb 3, 2014 at 4:41
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2 Answers
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The set $1^*+0^*$ is composed of two parts: $1^*$ and $0^*$. The first part, $1^*$, is all strings composed entirely of $1$s. The second part, $0^*$, is all strings composed entirely of $0$s. In contrast, $(1+0)^*$ is all strings composed of $0$s and $1$s. Can you now think of a string in $(1+0)^*$ but not in $1^*+0^*$?
answered Feb 3, 2014 at 4:13
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(1*+0*)= 11.. or 00... but cannot produce 101010101
(1+0)*= anything with 1 and 0
yeah: (1*+0*)* would be a different story.
