For the following language over Σ = {a, b}, provide a regular expression and a DFA for the language. Your automata should have at most 10 states.The set of strings that contain exactly three as and an even number of bs. For example, abababb is in the language, while ababab is not.

Construct an nfa with three states that accepts the language {ab, abc}∗

For each of the following languages over the alphabet Σ = {a, b, c} specified by the regular expressions (a)–(c),provide two strings in Σ∗ that are members and two strings in Σ∗ that are not members of the language (fourstrings each).(a) ab + a(b) ((bc)∗ + b)a(c) (a + ab + abc)∗(b + c)

Find dfa’s that accept the following languages:(a) L (aa∗ + aba∗b∗).

Which of the following languages are regular?A = {x | x has two 0’s separated by the number of positions that is a multiple of 4 }.B = {x | x is binary representation of multiple of 3}.C = {x | x is a binary string and decimal of any prefix of x is not of form 3m + 2, where m ≥ 0}.Select one:a. All of the mentioned.b. Only B and C. c. Only A.d. Only B.

Write regular expressions for the following languages.1. the set of all alphabetic strings;2. the set of all lower case alphabetic strings ending in a b;3. the set of all strings from the alphabet a, b such that each a is immedi-ately preceded by and immediately followed by a b