Question

If S = {xx, xxx}, and xxxxxxx ЄS*, than which of the following is factor of S:

a)xx|xx|xxx
b) xx|xxx|xx
c) both a and b
d) non of them

Answer 1

The set S = {xx, xxx}, and xxxxxxx ЄS* do not have any of the options given as a factor of the set. The correct answer is option d) none of them.

Step-by-step explanation:

The set S = {xx, xxx} consists of two elements: xx and xxx. The symbol Є represents the element belongs to the set.

So, when it is stated that xxxxxxx belongs to S*, it means that the string xxxxxxx is an element of the set S*, which is the set of all possible strings that can be formed using the elements of S, including repetitions.

To determine which of the given options is a factor of S, we need to analyze the structure of each option in terms of the elements of S that are present. Option a) xx|xx|xx represents three repetitions of the element xx, which can be formed using the elements of S.

Option b) xx|xxx|xx represents the elements xx and xxx, but it includes an additional element xxx that is not present in S. Option c) both a and b contains elements that can be formed using the elements of S, so neither option is a factor of S. Therefore, the correct answer is option d) none of them.