Question $1$:

Write Regular Expression of the following

a$.$ Language of all words that have at least two a$\text{'}$s

b$.$ Language of all words that have at least one a and at least one $b$

c$.$ Language of all words that have at least one $a$ or at least one $b$

d$.$ The languages $L,$ of even length, defined over $=\{a,b\}$

e$.$ The languages $L,$ of odd length, defined over

f$.$ The strings of length $2,$ starting with a

g$.$ The language of all words over the alphabet $a,b$

h$.$ All words ending with $b$

i$.$ All words that start with a

$j.$ The language of all strings, not beginning with $b$

k$.$ All words that start with a double letter

I. All words that contain at least one double letter.

m$.$ The language of all string not containing the substring $000$

n$.$ The language of all string that do not contain substring $110$

o$.$ The language of all strings containing both $101$&$010$ as substring

p$.$ The language of all strings in which both the number of $0\text{'}$s and the number of $1\text{'}$s are Even.

q$.$ The language of all strings in which both the number of $0\text{'}$s and the number of $1\text{'}$s are Odd.

r$.$ All words that contain Exactly two$1\text{'}$s or three $1\text{'}$s$,$ not more

s$.$ All string that have exactly one double letter in them

t$.$ All the word in which $1$ is tripled or $0$ is tripled, but not both

u$.$ All the String in which the total no of $1\text{'}$s is divisible by $3,$ no matter how they are arranged

such as $1101100101$

v$.$ All the words in which any $0\text{'}$s that occurs are found in clumps of odd number at a time, such

as $1101100010$