Let A$1,$ A$2,$ and A$3$ be languages defined over an alphabet $\backslash$Sigma $.$

a$.$ Define Majority$($A$1,$ A$2,$ A$3)=\{$w $|$ w is in at least two of $\{$A$1,$ A$2,$ A$3\}\}.$

b$.$ Show that Majority$($A$1,$ A$2,$ A$3)$ is regular if A$1,$ A$2,$ and A$3$ are regular.