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