Answer
(a)
As, \[\left( d\ \square \ e \right)=c\], thus
\[\begin{align}
& e\ \vartriangle \ \left( c\ \square \ d \right)=c\ \vartriangle \ c \\
& =e
\end{align}\]
Now, find RHS as,
\[\begin{align}
& \left( c\ \vartriangle \ d \right)\ \square \ \left( c\ \Delta \ e \right)=b\ \square \ d \\
& =e
\end{align}\]
Hence, \[e\ \vartriangle \ \left( c\ \square \ d \right)=\left( e\ \vartriangle \ c \right)\ \square \ \left( e\ \Delta \ d \right)\].
(b)
As, \[c\ \vartriangle \ \left( d\ \square \ e \right)=\left( c\ \vartriangle \ d \right)\ \square \ \left( c\ \Delta \ e \right)\]and\[c\]is distributed over \[\left( d\ \square \ e \right)\]. Thus, distributive property is used.
Hence, the distributive property is used in \[c\ \vartriangle \ \left( d\ \square \ e \right)=\left( c\ \vartriangle \ d \right)\ \square \ \left( c\ \Delta \ e \right)\].
