Let L$1,$ L$2$ and L$3$ be languages over some alphabet $\backslash$Sigma $.$ In each part below, state the relationship

between the given two languages. Are they equal, is one a subset of the other, do they have

an empty or non$-$empty intersection? Give reasons $($proof$!)$ for your answers, and counterexamples where needed.

$($a$)$ L$1($L$2\backslash$cap L$3)$ versus L$1$L$2\backslash$cap L$1$L$3.$

$($b$)$ L

$$

$1\backslash$cap L

$$

$2$

versus $($L$1\backslash$cap L$2)$

$$

$.$

$($c$)$ L

$$

$1$L

$$

$2$

versus $($L$1$L$2)$

$$

$.$

$($d$)$ L

$$

$1$

$($L$2$L

$$

$1$

$)$

$$ versus $($L

$$

$1$L$2)$

$$L

$$

$1$

$.$