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Binary operation/Table/4/2/Exercise
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On the set
M
=
{
a
,
b
,
c
,
d
}
,
{\displaystyle {}M=\{a,b,c,d\}\,,}
we consider the
binary operation
⋆
{\displaystyle {}\star }
given by the table
⋆
{\displaystyle {}\star }
a
{\displaystyle {}a}
b
{\displaystyle {}b}
c
{\displaystyle {}c}
d
{\displaystyle {}d}
a
{\displaystyle {}a}
b
{\displaystyle {}b}
a
{\displaystyle {}a}
c
{\displaystyle {}c}
a
{\displaystyle {}a}
b
{\displaystyle {}b}
d
{\displaystyle {}d}
a
{\displaystyle {}a}
b
{\displaystyle {}b}
b
{\displaystyle {}b}
c
{\displaystyle {}c}
a
{\displaystyle {}a}
b
{\displaystyle {}b}
c
{\displaystyle {}c}
c
{\displaystyle {}c}
d
{\displaystyle {}d}
b
{\displaystyle {}b}
d
{\displaystyle {}d}
d
{\displaystyle {}d}
d
{\displaystyle {}d}
Compute
b
⋆
(
a
⋆
(
d
⋆
a
)
)
.
{\displaystyle b\star (a\star (d\star a)).}
Does there exist a neutral element for
⋆
{\displaystyle {}\star }
?
Create a solution