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Question
Define an operation * on Q as follows: a * b = `(("a" + "b")/2)`; a, b ∈ Q. Examine the existence of identity and the existence of inverse for the operation * on Q.
Solution
a * b = `(("a" + "b")/2)`; a, b ∈ Q
For identity, a * e = e * a = a
Now; a * e = a
`("a"+ "e")/2` = a
a + e = 2a
e = 2a – a = a
Which is not possible
∴ Identity does not exist and hence the inverse does not exist.
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