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Question
Fill in the following table so that the binary operation * on A = {a, b, c} is commutative.
| * | a | b | c |
| a | b | ||
| b | c | b | a |
| c | a | c |
Solution
Given that the binary operation * is Commutative.
To find a * b:
a * b = b * a ........(∵ * is a Commutative)
Here b * a = c.
So a * b = c
To find a * c:
| * | a | b | c |
| a | b | c | a |
| b | c | b | a |
| c | a | a | c |
a * c = c * a ........(∵ * is a Commutative)
c * a = a. .......(Given)
So a * c = a
To find c * b:
c * b = b * c
Here b * c = a.
So c * b = a
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