The $\Delta$ operation on the set $\mathrm { A } = \{ \mathrm { a } , \mathrm { b } , \mathrm { c } , \mathrm { d } , \mathrm { e } \}$ is defined by the table below. For example, a $\Delta \mathrm { d } = \mathrm { c }$ and $\mathrm { d } \Delta \mathrm { a } = \mathrm { a }$.
$\Delta$
a
b
c
d
e
a
a
b
a
c
d
b
c
b
b
a
e
c
a
b
c
d
e
d
a
a
d
d
b
e
e
e
e
d
a
According to this table, which of the following subsets of set A
$\mathrm { K } = \{ \mathrm { b } , \mathrm { c } , \mathrm { d } \}$
$\mathrm { L } = \{ \mathrm { a } , \mathrm { b } , \mathrm { c } \}$
$\mathrm { M } = \{ \mathrm { c } , \mathrm { d } , \mathrm { e } \}$
are closed under the $\Delta$ operation? A) Only K B) Only L C) K and L D) K and M E) L and M
The $\Delta$ operation on the set $\mathrm { A } = \{ \mathrm { a } , \mathrm { b } , \mathrm { c } , \mathrm { d } , \mathrm { e } \}$ is defined by the table below. For example, a $\Delta \mathrm { d } = \mathrm { c }$ and $\mathrm { d } \Delta \mathrm { a } = \mathrm { a }$.
\begin{center}
\begin{tabular}{ l | l l l l l }
$\Delta$ & a & b & c & d & e \\
\hline
a & a & b & a & c & d \\
b & c & b & b & a & e \\
c & a & b & c & d & e \\
d & a & a & d & d & b \\
e & e & e & e & d & a \\
\end{tabular}
\end{center}
According to this table, which of the following subsets of set A
\begin{itemize}
\item $\mathrm { K } = \{ \mathrm { b } , \mathrm { c } , \mathrm { d } \}$
\item $\mathrm { L } = \{ \mathrm { a } , \mathrm { b } , \mathrm { c } \}$
\item $\mathrm { M } = \{ \mathrm { c } , \mathrm { d } , \mathrm { e } \}$
\end{itemize}
are closed under the $\Delta$ operation?\\
A) Only K\\
B) Only L\\
C) K and L\\
D) K and M\\
E) L and M