Automata and Complexity, Non Regular and Context Free Languages

$4.(8$ points$)$ Give a CFG for the language$\{($a$^($i$)$b$^($j$)|$x$,$y in N$,$ x$+$y$=$i$)$:$\}$ and $4$x$+3$y$=$j$\}.$

$5.(8$ points$)$ Prove that the regular languages are closed under set difference. If A$,$B are regular, then so is A$\backslash$B$=\{($w in$\backslash$Sigma $^(*)|$w in A$)$:$\}$ and w not in B$\}.$