The table of an operation $\Delta$ defined on the set $A = \{ 1,2,3,4,5 \}$ is given below.
$\Delta$
1
2
3
4
5
1
5
1
3
2
4
2
3
2
1
4
5
3
2
3
4
5
1
4
5
4
1
3
2
5
1
5
4
2
3
Also, for $\mathrm { a } \in \mathrm { A }$, the set $\mathrm { M } ( \mathrm { a } ) = \{ \mathrm { b } \in \mathrm { A } \mid \mathrm { a } \Delta \mathrm { b } = \mathrm { b } \Delta \mathrm { a } \}$ is defined. Accordingly, which of the following is the set $\mathbf { M } ( \mathbf { 4 } )$? A) $\{ 1,2,4 \}$ B) $\{ 1,3,5 \}$ C) $\{ 2,3,4 \}$ D) $\{ 2,4,5 \}$ E) $\{ 3,4,5 \}$
The table of an operation $\Delta$ defined on the set $A = \{ 1,2,3,4,5 \}$ is given below.
\begin{center}
\begin{tabular}{ l | l l l l l }
$\Delta$ & 1 & 2 & 3 & 4 & 5 \\
\hline
1 & 5 & 1 & 3 & 2 & 4 \\
2 & 3 & 2 & 1 & 4 & 5 \\
3 & 2 & 3 & 4 & 5 & 1 \\
4 & 5 & 4 & 1 & 3 & 2 \\
5 & 1 & 5 & 4 & 2 & 3 \\
\end{tabular}
\end{center}
Also, for $\mathrm { a } \in \mathrm { A }$, the set $\mathrm { M } ( \mathrm { a } ) = \{ \mathrm { b } \in \mathrm { A } \mid \mathrm { a } \Delta \mathrm { b } = \mathrm { b } \Delta \mathrm { a } \}$ is defined.
Accordingly, which of the following is the set $\mathbf { M } ( \mathbf { 4 } )$?\\
A) $\{ 1,2,4 \}$\\
B) $\{ 1,3,5 \}$\\
C) $\{ 2,3,4 \}$\\
D) $\{ 2,4,5 \}$\\
E) $\{ 3,4,5 \}$