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

## (a + b)* a (a + b)*

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

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

**Strings of length 1: **a, No other valid strings

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

**Strings of length 3: a**aa, aab, baa, bab, No other valid strings

** Strings of length 4:** aaaa, babb, aaab, baaa,……. and many other similar strings.

**Strings of length 5: a**aaab, aaaba, aaabb, abbba, aabaa, bbbaa,………and many other similar strings.

**Note:** Many other strings of lengths 6, 7, 8. 9, 10 11, ….etc which must have at least one a are valid. 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: **b, No other invalid strings

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

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

**Note:** All other strings defined over {a, b) that have no a are invalid strings. You can try it by yourself.

## Write a Regular expressions defined over {0, 1} for all non empty strings of odd length.

## (0 + 1)* 0 (0 + 1)*