Question:
Find the identity element in the set $I^+$ of all positive integers defined by $a * b = a + b$ for all $a$, $b \in I^+$.
Find the identity element in the set $I^+$ of all positive integers defined by $a * b = a + b$ for all $a$, $b \in I^+$.
Updated On: Jul 6, 2022
- $1$
- $2$
- $3$
- $0$
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The Correct Option is D
Solution and Explanation
Let $e$ be the identity element exist in the set of all positive integers w.r.t. $*$ on $I^*$.
Then, $a*e = a \,\forall \, a \in I^+$
$\Rightarrow a + e = a$
$ \Rightarrow e = 0$
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