Show how to define the following languages over $\backslash$Sigma $=\{0,1\}$ using only $\backslash$epsi $,$ the

alphabet symbols $0$ and $1,$ and the operations of union, concatenation, and closure.

Note: Your answer cannot use the intersection or complementation operation.

Below $$or$$ always means $$inclusive or$.$

$($a$)$ All strings that have $0000$ or $1111$ as a substring.

$($b$)$ All strings that have both $00000$ and $11111$ as a substring.

$($c$)$ All strings that have an odd number of occurrences of the symbol $0.$

$($d$)$ All strings w satisfying condition $($i$)$ or condition $($ii$)$:

$($i$)$ w has at most three occurrences of $0$;

$($ii$)$ w has at most three occurrences of $1.$

$($e$)$ All strings that begin with $0$ and end with $0$ and do not have $010$ as a substring