Question

Find the identity element in the set $I^+$ of all positive integers defined by $a * b = a + b$ for all $a$, $b \in I^+$.

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

Answer: (D)

$0$

Answer 2

Let $e$ be the identity element exist in the set of all positive integers w.r.t. $*$ on $I^*$. Then, $a*e = a \,\forall \, a \in I^+$ $\Rightarrow a + e = a$ $\Rightarrow e = 0$