Which of the following strings do not belong to the given regular expression?…

Regular Expression Analysis

The given regular expression is (a)*(a+cba). This can be broken down into two main parts:

• (a)*: Represents zero or more occurrences of the character 'a'.

• (a+cba): Represents a choice between the character 'a' or the sequence 'cba'.

Therefore, valid strings must consist of any number of 'a's followed by either a single 'a' or the sequence 'cba'. This effectively means the string must end in 'a' (if the first part is used) or 'cba' (if the second part is used), with only 'a's preceding them.

Evaluation of options:

• acbca: Contains 'b' before the final 'a' and does not end in 'cba'. Invalid.

• aaa: Consists of 'a's followed by 'a'. Valid.

• acba: Consists of 'a' followed by 'cba'. Valid.

Conclusion: The string 'acbca' does not belong to the language defined by the regular expression.