Let L$1,$ L$2$ and L$3$ be languages over $\{0,1\}*.$ In each case below, two languages are given. Say what

the relationship is between them. $($Are they always equal? If not, is one always a subset of the

other?$)$ Give reasons for your answers, including counterexamples if appropriate.

a$)$ L$1($L$2\backslash$cap L$3),$ L$1$L$2\backslash$cap L$1$L$3$

b$)$ L$1*\backslash$cap L$2*,($L$1\backslash$cap L$2)*$

c$)$ L$1*$L$2*,($L$1$L$2)*$