[離散]第九章代數結構 精選範例 4

有疑問之題目如下
For each of the following cases, determine whether the set under the binary
operation * forms a semigroup or a monoid. Please explain why.
(2) The set of finite sequences of 0's and 1's containing an even number of 1's with *denoting the catenation operation

我的疑惑在於題目只說1's 為containing an even number of 1's

但是沒有說明0's

解答也沒有用到 0's

還是說題目的0's事來搗亂的?

麻煩幫我解答囉~
謝謝