## Write a Regular expressions defined over {a, b} for All strings with at least one a and at least one b.

### (a + b)* (ab + ba) (a + b)*

__Valid strings: (must be accepted by our Regular Expression)__

__Valid strings: (must be accepted by our Regular Expression)__

**Strings of length 1: **No valid strings

**Strings of length 2:** ab,ba, No other valid strings

**Strings of length 3: a**ab, aba, bab, bba,……. and many other similar strings.

** Strings of length 4:** aabb, baab, abab, baba,……. and many other similar strings.

**Strings of length 5: a**baab, ababa, aaabb, ababa, aabab, bbaaa,………and many other similar strings.

**Note:** Many other similar strings of lengths 6, 7, 8. 9, 10 11, ….etc that have at least one a and at least one b are valid strings. You can try it by yourself.

__Invalid strings: (must be Rejected by our Regular Expression)__

__Invalid strings: (must be Rejected by our Regular Expression)__

**Strings of length 1: **a, b No other invalid strings

**Strings of length 2:** aa, bb, No other invalid strings

**Strings of length 3: **aaa, bbb, No other invalid strings

**Note:** All other strings defined over {a, b) that not have at least one a and at least one b are invalid strings. You can try it by yourself.

## Write a Regular expressions defined over {0, 1} for All strings with at least one a and at least one b.

### (0 + 1)* (01 + 10) (0 + 1)*

## More Examples of Regular Expression

- Regular Expression for no 0 or many triples of 0’s and many 1 in the strings.
- RegExp for strings of one or many 11 or no 11.
- Regular expressions for all non empty strings
- Regular expressions over {a, b} for all non empty strings of even length
- Regular expressions for all non empty strings of odd length
- A regular expression for ending with abb
- A regular expression for all strings having 010 or 101.
- Regular expression for Even Length Strings defined over {a,b}
- Regular Expression for strings having at least one double 0 or double 1.
- Regular Expression of starting with 0 and having multiple even 1’s or no 1.
- Regular Expression for an odd number of 0’s or an odd number of 1’s in the strings.
- Regular Expression for having strings of multiple double 1’s or null.
- Regular Expression (RE) for starting with 0 and ending with 1.
- RE for ending with b and having zero or multiple sets of aa and bb.
- A regular expression of the second last symbol is 1.
- RE for starting with 1 having zero or multiple even 1’s.
- Regular Expression for multiple a’s and multiple b’s.
- RE for exactly single 1 many 0’s |exactly single a many b.
- A regular expression for strings starting with aa and ending with ba.
- A regular expression for the language of all consecutive even length a’s.
- A regular expression for the language of all odd-length strings
- A regular expression for the language of all even length strings but ends with aa.
- A regular expression for the language of an odd number of 1s.
- A regular expression for the language of even length strings starting with a and ending with b in theory of automata.
- A regular expression for the language of all even length strings but starts with a.
- A Regular Expression for the Language of all strings with an even number of 0’s or even number of 1’s.
- A regular expression for the language of all those strings end with abb.
- A regular expression for string having must 010 or 101.
- Regular expression of strings begin with 110

Regular expression of strings begin and end with 110

Regular expression of strings containing exactly three consecutive 1’s. - A Regular Expression of all strings divisible by 4.
- A Regular Expression Strings that does not contain substring 110.
- Regular expressions for all strings with at least one a
- Regular expressions for all strings with at least two a’s
- Regular expressions for All strings with exactly two b
- Regular expressions for at least one a and at least one b