Pumping Lemma for regular sets

a$.$ State the Pumping Lemma for regular sets.

b$.$ Use the Pumping Lemma to prove that the set A$=\{$a$^($n$)$b$^($m$)$c$^($p$)|$n$,$m$,$p$>=0,$n$+$m$=$p$\}$ is not regular.

c$.$ Use the Pumping Lemma to prove that the set B$=\{$xin$\{$a$,$b$,$c$\}^(*)|$#a$($x$)<$#b$($x$)<$#c$($x$)\}$#a$($x$)$ is the number

of occurrences of the symbol a in string x