Find the identity element in the set I+ of all positive integers defi

1.	Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.
Answer» Let e be the identity element in I⁺ with respect to * Such that, a * e = a = e * a, ∀ a ∈ I⁺ a * e = a and e * a = a, ∀ a ∈ I⁺ a + e = a and e + a = a, ∀ a ∈ I⁺ e = 0, ∀ a ∈ I⁺ Hence, 0 is the identity element in I⁺ with respect to *.

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

Answer»

Let e be the identity element in I⁺ with respect to *

Such that, a * e = a = e * a, ∀ a ∈ I⁺

a * e = a and e * a = a, ∀ a ∈ I⁺

a + e = a and e + a = a, ∀ a ∈ I⁺

e = 0, ∀ a ∈ I⁺

Hence, 0 is the identity element in I⁺ with respect to *.