Final answer:
The regular expressions abcφ (abc followed by empty string) and abc(φ)* (abc followed by zero or more occurrences of the empty string) are equivalent because multiple occurrences of the empty string are still equivalent to the empty string.
Step-by-step explanation:
The student is asking whether the two regular expressions abcφ and abc(φ)* are equivalent. In regular expressions, φ is often used to denote the empty string, and the * operator denotes zero or more occurrences of the preceding element. Therefore, abcφ is a regular expression matching the string "abc" followed by nothing (the empty string), while abc(φ)* matches the string "abc" followed by zero or more occurrences of the empty string. Since multiple occurrences of the empty string are still nothing, these two regular expressions are indeed equivalent.
The two regular expressions abcφ and abc(φ)* are equivalent false.The regular expression abcφ matches the string abc followed by any character or no character at all. So, it can match strings like abc, abcd, or abcdef.On the other hand, the regular expression abc(φ)* matches the string abc followed by zero or more occurrences of φ. Since φ represents an empty string, this expression can match strings like abc, abcφ, abcφφ, and so on.Therefore, these two regular expressions are not equivalent, as they match different sets of strings.