Answer:
Given
a*b =
The
composition table for operation * is as follows :
From
the composition table, it is clear that 0 * 0 = 0, 0 * 1 = 1, 0 * 2 = 2, 0 * 3
= 3 0 * 4 = 4, 0 * 5 = 5.
*
0
1
2
3
4
5
0
0
1
2
.3
4
5
1
1
2
3
4
5
0
2
2
3
4
5
0
1
3
3
4
5
0
1
2
4
4
5
0
1
2
3
5
5
0
1
2
3
4
is an
identity element or the operation *.
2n
part : Let
be
any element of set {0, 1, 2, 3, 4, 5}
Therefore,
there exists an element 6 ? a of set {0, 1, 2, 3, 4, 5} such that
a
* (6 ? a) = a + 6 ? a ? 6 = 0
and
(6 ? a) * a = 6 ? a + a ? 6 = 0
i.e.,
a * (6 ? a) = (6 ? a) * a = 0
is the
inverse of a.
Also
0 * 0 = 0 + 0 = 0
is inverse
of itself.
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