Give the recursive definition of the following languages. For both of these you should concisely

explain why your solution is correct.

$1.$ A language that contains all strings.

$2.$ A language which holds all the strings containing the substring $000.$

$3.$ A language LA that contains all palindrome strings using some arbitrary alphabet $\backslash$Sigma $.$

$4.$ A language LB that does not contain either three $0$s or three $1$s in a row. E$.$g$.,001101$ in LB

but $10001$ is not in LB