\(A=\frac{7}{19}.\frac{8}{11}+\frac{7}{19}.\frac{3}{11}+\frac{12}{19}\)

\(=\frac{7}{19}.\left (\frac{8}{11}+\frac{3}{11} \right )+\frac{12}{19}\)

\(=\frac{7}{19}.1 +\frac{12}{19}=1\)

\(B= \frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)

\(=\frac{5}{9}.\left (\frac{7}{13}+\frac{9}{13}-\frac{3}{13} \right )\)

\(=\frac{5}{9}.\frac{7+9-3}{13}\)

\(=\frac{5}{9}.\frac{13}{13}\)

\(=\frac{5}{9}.1=\frac{5}{9}\)

\(C=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).\left (\frac{1}{3}-\frac{1}{4}-\frac{1}{12} \right )\)

\(=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).\frac{4-3-1}{12}\)

\(=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).0=0\)