Prove or disprove the following:

$1.$ For all languages L$1,$ L$2$; $($L$1\backslash$cup L$2)=$ L$1\backslash$cup L$2.$

$2.$ For all languages L$1,$ L$2,$ L$3$; $($L$1\backslash$cup L$2)$L$3=($L$1$L$3)\backslash$cup $($L$2$L$3).$

$3.$ For all languages L$1,$ L$2,$ L$3$; $($L$1$L$2)\backslash$cup L$3=($L$1\backslash$cup L$3)($L$2\backslash$cup L$3)$

For a proof, give a careful mathematical argument, based on the formal definitions of subset, concatenation, etc. For a disproof, give a specific, concrete, example of languages L$1,$ L$2,$ L$3.$