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

Question

Philoid · Accepted Answer

Given that binary operation ‘*’ is valid for set ‘I ⁺ ’ of all positive integers defined by a*b = a + b for all a,b∈I ⁺.

Let us assume a∈I ⁺ and the identity element that we need to compute be e∈I ⁺.

We know that he Identity property is defined as follows:

⇒ a*e = e*a = a

⇒ a + e = a

⇒ e = a – a

⇒ e = 0

∴ The required Identity element w.r.t * is 0.

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