A binary operation \(*\) is defined on the set, R, of real numbers by \(m * n = m + n + 2\). Find the : (a) identity element under the operation ; (b) inver...
Question 1 Report
A binary operation \(*\) is defined on the set, R, of real numbers by \(m * n = m + n + 2\). Find the :
(a) identity element under the operation ;
(b) inverse of n under the operation .
Answer Details
The operation is \( m * n = m + n + 2 \).
(a) Identity element. Let \(e\) be the identity, so \( m * e = m \) for all \(m\):
\[ m + e + 2 = m \Rightarrow e = -2. \] The identity element is \( e = -2 \).
(b) Inverse of n. Let \(n^{-1}\) be the inverse, so \( n * n^{-1} = e = -2 \):
\[ n + n^{-1} + 2 = -2 \Rightarrow n^{-1} = -4 - n. \] The inverse of \(n\) is \( n^{-1} = -(n+4) \).
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