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Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations2 Marks
Question
Determine whether the following operations define a binary operation on the given set or not:
'×6' on S = {1, 2, 3, 4, 5} defined by, a ×6 b = Remainder when ab is divided by 6.
✓

Answer

Consider the composition table,
×6
1
2
3
4
5
1
1
2
3
4
5
2
2
4
0
2
4
3
3
0
3
0
3
4
4
2
0
4
2
5
5
4
3
2
1
Here all the elements of the table are not in S.
For a = 2 and b = 3,
$\text{a}\times_6\text{b}= 2\times_63$ = remainder when 6 divided by $6=0\neq\text{S}$
Thus, ×6 is not a binary operation on S.

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